5

Determine the quadratic function whose graph is given.The vertex is (1, 2) The y-intercept is (0 , 5).flx)(Simplify your answer )...

Question

Determine the quadratic function whose graph is given.The vertex is (1, 2) The y-intercept is (0 , 5).flx)(Simplify your answer )

Determine the quadratic function whose graph is given. The vertex is (1, 2) The y-intercept is (0 , 5). flx) (Simplify your answer )



Answers

For quadratic function, identify the vertex, axis of symmetry, and $x$- and $y$-intercepts. Then, graph the function.
$y=(x+1)^{2}-5$

We are given the function. Why equals negative X plus one square X plus one quantity square minus five and first gonna find the Vertex. So the vertex are our function. Okay, looking at this, do we have it in Vertex form? Well is in the form a times X minus H squared plus cape. I'm saying yes, it is our is negative one. And then we have an X plus one. You know, we don't have X minus some constant, but again, X plus one can be thought of as X minus in negative one. So our h is negative one and then we have one negative five. But then native five we thought of as plus a minus five. So our H value is negative one and our k is negative. Um is negative five? Yeah, because again, remember, it is always X minus h squared and then plus cake. So we have x minus in negative one and then plus a negative five. So you always rewrite addition and subtraction and vice versa. Okay, just doesn't for text And then our access of symmetry access of symmetry is the line that goes right through the vertex. So our It's always a vertical line, which is are gonna be X equals something. And the accident symmetry is just the F value is just the X value of, um, the Vertex. Right, because X equals negative one. It's just a vertical line that goes right to the Vertex. So that is our access of symmetry, and they find the X intercepts. So the X intercepts. Okay, so that's where the parabola is gonna across the X axis. Well, the, um, we're crosses the X axis. The value of why is zero right? It wouldn't across the X axis. You have an X value there, but then you why? Value is zero. It is going across the X axis. There's no height on the function, so the y value there is zero. So find the X intercepts. All we do is set our function equal to zero. You set Why are set the function equal to zero and then find what value of X makes the function equals zero. We have zero equals negative X plus one squared minus back. And then we just solve this thing for X. So when a mover constant overs, we add five to both sides to get five equals Negative. X plus one. Ah, squared. Okay. Um okay. And then, well, we can we can What? We have a negative sign in front of the X plus ones. I want to the square root off this whole thing with south for X. But first, I want it with that natives of the binding both sides of multiple and multiplying both sides by a negative one would give me a negative five. He close Well, X plus one squared, huh? And then, well, then the south for acts. What I would do is take the square root of both sides to get rid of the prophecies because the square root of X plus one square is excellence one. But then I would have take the square root of negative five. And, uh oh, I can't take the square root of a negative number in the real numbers. So that means you can't do it. That means that the X intercepts do not exist. So there are no X intercepts. This problem never crosses the X access. So therefore the X intercepts we could say do not exist does not exist. Capital d n e means does not exists for okay, Means does not exist. So, um, looking back at our original I mean function here we see that I mean, this is a shift of X squared the left eye one unit, and then it shifted down. It's just because of the minus five outfront minutes, it shifts down. Meaning it's kind of the vertex. What we said, we see the Vertex is negative. One negative vibes. The Vertex is beneath the X axis. Okay, so the Vertex is beneath the X axis and it opens downward because of the negative sign out front. So if we're beneath the X access and we open downward, could we ever cross the X axis? Think about it. No, we can't. So you couldn't do it this way and find out that you can't take the square root of a negative number. That means the X intercepts don't exist. Or you can realize where the Vertex is and then doesn't open up or down. And then what could it possibly across the X axis? If it can't, there are no X intercept. So there's two possible the student a ways to go about seeing that the X intercepts do not exist. Okay, then, to find the y intercept while the Y intercept is just, um, where it crosses the y axis. So the X values there are zero so far the Y intercept we just set. We set X equal to zero, and we saw for why? So we have Why equals negative? Um, you said X equals zero. So zero plus one square minus five. OK, zero plus one is just one. So we got Why equals? Well, negative. You never find out. Front zero plus one is one. So we have one while one squared. If one gay square that's gonna be one minus five. So once we're just one. But there's a native native sign out front that's minus one times one, which is minus once we have equals minus one at the minus one. Because this is you kind of square. This first. That's positive one. But then it's time to minus one, which is minus one so minus one minus five and minus four minus five equals minus six. So the Y intercept the wine is up we see is negative. Six. That's the 60.0 comma. Negative. Six. All right, so then Let's grab this thing. Let's grab this thing's racist restroom, But pretty, pretty, pretty, pretty, pretty big did. Okay, And now, um, graph. So here's our X Y axes. We got our Vertex and negative one negative five. So negative 11 unit down. Five units down. Let's say right about here. This is the point. Um, negative one negative five is right here. And then we've got, um we don't have any ex intercepts, but why has a negative sex so negative Sex is down. Let's say this is negative. Five. So negative. Sex me down. Some of it about here. Okay. And we know that we opened downward, right? Because a day that was negative ones. We opened downward like this, and we can see that would go on forever. This probably will never right. Never, ever, ever cross the X access. Therefore, like we already saw, we do not have any ex intercepts. All right, There you go. See it

So here we are, given the function, why is equal to negative X Square plus five And first we were asked to find the Vertex. So here we have a quadratic function, which for graph it would be a Baramula. So trying to find the Vertex of the problem while looking at this function, we should notice that it is well if it waas in Vertex form a times X minus H square. Okay, we're just given the Vertex, which is the Vertex would be the point H comma Kate, What is this in Vertex form? Well, we just have we saw before. We always have, like, some coefficient in front. And then we had either an X minus some constant or X plus some constant. Or we saw that that, like quantity and you saw that whole thing square. But here we only see x square. But well, can I write this as X minus some constant square? Oh, sure, right. I could rewrite this as just negative instead of just x squared. I could write it as X well minus zero or explosive. But I'm running his X minus zero squared and then plus five because now we see that we have some core fishing in front that's negative one times X minus, some constant, so X minus h squared and then plus some constant. So again, if it's in a times X minus H Square plus K, the Vertex is always the point. H comma Kate that your X y point. So the fact that it's already X minus something so x minus h. The H is just zero. So our vertex is at the 0.0 comma or zero comma. Five. Because we're plus five and it's a times X minus h squared plus cake. We already have a plus here, so it's plus five. So fighters came. So our Vertex is at the 0.0 kind of five. Then we were asked to find the access of symmetry. So the axis of symmetry is just It's the line, the vertical line that goes right through the Vertex. So if the Vertex is at the 0.5 the axis of symmetry is a vertical line, so it'll always be X equals something, and it's just X equals the extra symmetry Just X equals the X value of the Vertex. So the vertex that the 0.5 The axis of symmetry is just the equation. X equals zero. All right, um, and then were asked to find the x intercepts. So the X intercepts? Well, that's where this problem, um, crosses the X axis. Right? And we cross wherever we cross the X axis, while the corner of that point B why value there would have to be zero. So to find the x intercepts and go back to our original function and just set the function or set, why equal to zero? So if we set the function equal to zero and have zero equals negative x squared plus five that we just sell for X and find the values of X that make this true And that would be the values of X when y zero. And that would be our ex insects. So to solve this well, we have a constant. We have negative X squared plus five in our constant five on the sides. We can, um we can subtract five from both sides. If we do that, we'll left with negative five negative five equals, um, negative X square, because we subtracted five from both sides of that five is gone. Okay, then we have while we have some excluded, we have negative X squared so we can multiply or divide. Same thing. Really? Um, both sides by a negative one. And that's just going to change the signs on both sides of the equation stories. And we would have five five equals a positive X squared. And then, well, to find X right, we have five equals X squared. If you take the square root of X squared, or we can start the square and we're left with X. So if you could do the same thing, the both sides of an equation, you must do you know anything? We want lunch as long as you do the same thing that both sides he was taking the square root of both sides of the equation. So the squared of X squared is just going to be X and square to five. Well, that's the square root of five. Right square to five is a rational number. Oops. Whoops. Whoops. Whoops, Ists. That's try to fix that. Go back here. Did you Did you dio see if we can erase that? There we go. All right. From the time So I got the square X is just equal to the square root of fives. Okay, So is that Is that it? There's X equals grow to five. Well, at this step right here that we're taking the square root of X square, you get acts, but we take the square root of the constant on the other side of your equation, you're always going to get a plus or a minus because I have to square to five and I square it. I get five. But if I have negative the square root of five negative square root of five and I square that I also get five, so X is equal to plus or minus the square root of five. So therefore, my ex intercepts I get to values I get either Well, I get negative the square root of five, or or and I also get on the square defying. So there's my two x intercepts and then we're has to find the Y intercept where the Y intercept is. Where this problem is that across the why access and we're across the Y axis, while the value of X is equal to zero, right so defined the y intercept. We just going We substitute zero in our original equation and then find Well, what is the y value there when X is zero. So we just have we have why equals? Well, negative X squared. So I have Well, I guess you could write this as negative zero squared. I'm just plugging zero in for X. So native zero squared plus, um five. Well, zero square it is zero. Right? And the native sign up front here doesn't really matter, because negative zero is still zero. So why is just equal to five? So why is it gonna five? So therefore, my why intercept is five. And what point is that right? That's that's when x zero with winds up its five. That means the Y intercept is at the 50.0 comma five. So why is it is five and then we just asked a graph this thing. So once we have all this information, I mean graphing, it goes very quickly because we just we draw our X y axes here. All right, we're given that the Vertex now is at the 0.5 So 05 So that's we're on the Y axis 05 is right there on the axis of symmetry. Right. X equals zero. That is the Y axis. And then our X intercepts are square 25 and negative square to five. So square to five is, um what is that? That's a little bit bigger than to write. This quote affords to 3 to 5. Must be a little bigger than to someone over here. And then negatives grow to five. That's a little bit, um, less than negative two for somewhere over here. And then, um, why isn't this five? So again, if we're on the Y axis, if he accepts symmetry is the y axis. Why intercept is it doesn't make crossed up. Why? Access only crosses at the Vertex. So the why intercept in this case is the Vertex. And then, well, we just basic connect. The dots were also given that, um, our a value right. The coefficient in front is a negative one. We have negative X squared plus five. That's negative. One or negative one times. When I think of it as negative one times X minus zero squared plus five. And for tax form, the A is a negative one. So if is negative, that means problem. This problem is opening downward. So opening downward and again because, um, our vertex is above the X axis, and we're opening downward, then with death. Definitely gonna have X intercepts as we've seen before. We don't always have X intercepts. Um, right, if let's say if the vertex was above the x axis and perhaps open upward, then you would see that this thing would never, um, cross over the x axis. But, um but yeah, way. Have you already found them? So, um yeah, that's it for this problem and Ah, yeah, Take care. I'll see you soon.

For this exercise. We know that a quadratic function goes through the Vertex of 54 and passes through the point to negative four, and we're going to determine the equation of such a function. We start by writing that F of X is equal to its standard form eight times x minus h squared plus K that on the next line we can write f of X equals eight times first, all right X and then go back to the Vertex because this is a positive five will always take its opposite to produce a negative five here and square that resulting group. Then for the second portion plus K, we directly copy in the second coordinate of the Vertex along with this sign. So we'll have a plus four here for the next step as soon as we determine that value of a our work is going to be complete. And that takes us back to the fact that this function is going to pass through the point to negative four Sophie right effort to this will be equal to negative four and the left hand side with ff two. We're going to make a substitution where x takes on the value of two. We have a times to infer X minus five squared plus four equals negative fourth. So first inside the group, we have negative three Squared, which results in a positive nine times. A plus four is equal to negative four. Subtracting four from both sides, then gives us nine times a equals negative eight. And so now we know that A is negative Eight nights through division. Let's go back to this left column, where it we can now write the answer, which is f of X equals in place of a put in negative 8/9. Then that would multiply of the group X minus five squared plus four.

Using properties of the equation. We know that the Vertex of this particular parable will be at the point minus one comma five.


Similar Solved Questions

5 answers
Give a limit expression that describes the left end behavior of the function41x +Ax2 f(x) = 6 16x1 3XIim f(x) X+ 0J(Simplify your answer )
Give a limit expression that describes the left end behavior of the function 41x +Ax2 f(x) = 6 16x1 3X Iim f(x) X+ 0J (Simplify your answer )...
5 answers
Mechanism for the saponification of methyl acetate using Draw detailed, "curved arrow" NaOH:
mechanism for the saponification of methyl acetate using Draw detailed, "curved arrow" NaOH:...
5 answers
Find the annual percentage yield (APY) in the following situationA bank offers an APR of 4.46% compounded monthly:The annual percentage yield is (Do not round until the final answer: Then round t0 two decimal places as needed:)
Find the annual percentage yield (APY) in the following situation A bank offers an APR of 4.46% compounded monthly: The annual percentage yield is (Do not round until the final answer: Then round t0 two decimal places as needed:)...
5 answers
Anton Chapter 1, Section 1.5, Question 22
Anton Chapter 1, Section 1.5, Question 22...
5 answers
The slope of the tangent line to the parabola y = 31? Sx + 6 at the point2,8) is:PreviewThe equation of this tangent line written in point-slope form; (y yl) = m (x cl) is:Preview
The slope of the tangent line to the parabola y = 31? Sx + 6 at the point 2,8) is: Preview The equation of this tangent line written in point-slope form; (y yl) = m (x cl) is: Preview...
5 answers
Temperature decrease 0f 50 €? is equalto temperature decrease of25 Fo50 K50 Fo25 K
Temperature decrease 0f 50 €? is equalto temperature decrease of 25 Fo 50 K 50 Fo 25 K...
5 answers
(d) Assume that {he avcrage Ilfc of & color TV 8.6 Years with standard deviatlon years before brcaks: Suppose that & company quarantecs coror TVs and will replace = TV thut breuks while under guarantce wlth = Lnaytone Howevet; the company dous not wunt replace more than 633 of bhe Tlundcr quarantce. for how Jon9 = should thc quarantcc bc mede (rounded the neerest tenth ycar)?
(d) Assume that {he avcrage Ilfc of & color TV 8.6 Years with standard deviatlon years before brcaks: Suppose that & company quarantecs coror TVs and will replace = TV thut breuks while under guarantce wlth = Lnaytone Howevet; the company dous not wunt replace more than 633 of bhe Tlundcr qu...
5 answers
Calculate the pH ofa 0.067 M HC2H3Oz solution. The Ka for HCzH3Oz is equal to 1.8 x 10-5.
Calculate the pH ofa 0.067 M HC2H3Oz solution. The Ka for HCzH3Oz is equal to 1.8 x 10-5....
5 answers
228Th source is labeled 4.50 mCi, but its present activity is found to be 4.16 X 107 Bq: What is the present activity in mCi?Answer:CheckIf the half life of 228Th source is 1.91 years _ how long ago (in years) did it actually have 4.50 mCi activity?Answer:
228Th source is labeled 4.50 mCi, but its present activity is found to be 4.16 X 107 Bq: What is the present activity in mCi? Answer: Check If the half life of 228Th source is 1.91 years _ how long ago (in years) did it actually have 4.50 mCi activity? Answer:...
5 answers
What must be the ratio of the slit width to the wavelength for a single slit to have the ?7th diffraction minimum at 0-508:UlgsJl
What must be the ratio of the slit width to the wavelength for a single slit to have the ?7th diffraction minimum at 0-508 :UlgsJl...
5 answers
Signment Score:72.900ResourcesGive Up?FeedbackResumeestion of 12Attempt 1Evaluate the integral. (Use symbolic notation and fractions where needed: Use €C for the arbitrary constant: )sin- ( In (x)tan" (In(x)) dx 3x2sin- ( (In (x) ) -TCIncorrectQuestion Source: Rogawski Calculus Early TranscendentalsPublisher
signment Score: 72.900 Resources Give Up? Feedback Resume estion of 12 Attempt 1 Evaluate the integral. (Use symbolic notation and fractions where needed: Use €C for the arbitrary constant: ) sin- ( In (x) tan" (In(x)) dx 3x 2sin- ( (In (x) ) - TC Incorrect Question Source: Rogawski Calcu...
5 answers
The electric field between tvo parallel plates increasing which induces magnetic field If the rale, at which the electric field is increasing. increases, what happens to the magnilude of the induced magnelic field? DoesAncreaseDedeaseRemain the same
The electric field between tvo parallel plates increasing which induces magnetic field If the rale, at which the electric field is increasing. increases, what happens to the magnilude of the induced magnelic field? Does Ancrease Dedease Remain the same...
5 answers
In a Northwest Washington County; the speeding fines are determined by the formula: F(8) = 12(8 55) + 90 F(e) is the cost, in dollars, of the fine if a person is caught driving at a speed of miles per hour: where If a fine comes to 8474,how fast in mph was the person speeding?
In a Northwest Washington County; the speeding fines are determined by the formula: F(8) = 12(8 55) + 90 F(e) is the cost, in dollars, of the fine if a person is caught driving at a speed of miles per hour: where If a fine comes to 8474,how fast in mph was the person speeding?...
5 answers
Explain the reasons reason for using F-test in and not to use T-test in ANOVA?
Explain the reasons reason for using F-test in and not to use T-test in ANOVA?...
4 answers
TrainingLiburan TunjanganBonusGaji978986377693998382215486817978
Training Liburan Tunjangan Bonus Gaji 97 89 86 37 76 93 99 83 82 21 54 86 81 79 78...
5 answers
Question 36 Starch solution in Benedict's test is Not = yet answered Marked out of Select one: 1.00 a. negative result Flag question b. positive result positive control
Question 36 Starch solution in Benedict's test is Not = yet answered Marked out of Select one: 1.00 a. negative result Flag question b. positive result positive control...

-- 0.053654--