5

2 Graph the equationy = x2 + 4x + 3. Show the x-interceptfs);, Y- intercept(s), axis of symmetry; and vertex5, 3...

Question

2 Graph the equationy = x2 + 4x + 3. Show the x-interceptfs);, Y- intercept(s), axis of symmetry; and vertex5, 3

2 Graph the equationy = x2 + 4x + 3. Show the x-interceptfs);, Y- intercept(s), axis of symmetry; and vertex 5, 3



Answers

Use the vertex and intercepts to sketch the graph of each equation. If needed, find additional points on the parabola by choosing values of y on each side of the axis of symmetry. $$x=(y+2)^{2}-3$$

We have a number 22 in which fell apart with the the question off horizontal parabola which x equal to why plus two Whole square minus three. This is whole squared. Minus three. Okay, so now we need to compare this religious gender equation off. Dental parabola. They should be. Why mine escape bliss etch. Okay. So it will be equal to one. Because here is one which is greater than zero. So parabola will be opening. Right? Were like this. Vortexes. What exists at common K that is minus three comma minus two. This is the Vertex for X intercept. We will live plugging in what I call to zero. So in this equation, so x equal toe do a square minus three. It is forward minus 30 equal to one for months, equal to one. So x intercept will be one comma zero. This is our X intercept for Why intercept? Will we plug in X equal to zero for Why intercept? We were re plugging in x equal to zero in are given a question which is zero equal toe y plus tool square minus tree. This will be why plus two moles critical to three So why apply? Streak will toe less minus under three. So why would be equal toe minus to plus minus under three. Okay, on this under three. So why just upside? Zero comma minus two, minus under three and zero comma minus to bless Andrew three. These are the Y intercepts, so we can easily see that this lies between minus four to minus five minus eight to minus four. And this lies between zero to minus one. So it is drawn. The graph. This is why this is X. So where? Texas is minus three co minus two. This is minus T. This is minus two. So here it will be minus three comma minus two. Vertex X intercept is one comma, zero accent. Disip days. This is one. So one committee will be there. Accent just sipped. Why? Intercept is why intercepts are there to intercept. Minus two minus root three some minor. 3.74 between minus three to minus four. If this is minus three this in minus four to somewhere here. It will be minus stool minus through three. And the second is minus two plus two or three. It must be between 0 to 1 yet it should be minus two. And this is minus tool. Blessed with three. So our graph should look like this.

So, uh, just grab a lot of the equation is X equals Why minus two squared. Plus, we have to graph it using off course the Vertex and intercept. So from the standard form, we remember the H and K. Remember, Kay has to be opposite science their equal to three group. So in the graft, and two would be here, the protects of the parable, looking at the sign off a sign in front because it's positive the problem will open to the right with that vortex already now have no Why intercept? So, sir, calculate the X intercept said the accident opposable y equals zero zero minus two, which is negative. Squared three will be negative. Two squared. It's 4437 So the point will be seven years and there's no why intercept? So we go to the graph and look at it. Seven. In the wrong that opening we could, uh, graph that two parts of the parappa opening to the rights and the wind for sex and ah, that's the solution

We have phone number 26 in which we have been provided with the question and for gentle parabola, which is X equal toe y minus two whole squared plus three. Let us compare this with X equal to E. Why? Minus k hole square pass set. So we will be having equal to one, which is good. Run zero. So, parable, I will be opening right work. Okay, so where takes will be at comma K at history, from a case to so vortexes. Take a minute. Now forex intercept. We will look like in. So I called zero. So actually equal to minus two a squirrel plus three that is seven. So, accent, it's absurd. Only one there is one X intercept. Seven comma Zito for Why? Into sipped We will be plugging in X equal to zero. So zero equal to why minus two. Whole square. Blustery, which is over I minus tools critical to minus three, but squared off. Anything can not be negative. So there will be No Why Intercept? No. Why? Intercept letters. Draw the parable and now exit the vortexes over Texas three common to If this is three, this is too. So Vertex will be three comment. Oh, and X intercept days Exodus Every seven comma zero. So if this is seven comma zero Okay, so this is the aquatic way and require graph. Thank you so much.

So in this example, were given the equation to buy Squared Plus three. And this looks a little bit different than the general form because they don't have those parentheses where the K value typically is. If it's helpful, we can actually rewrite this. And since there's no que value, what that means is the cable. He's actually zero. If it helps you to look at it like this, that's easier to see So that the cave guys actually zero, they just didn't write it because you don't really need to write plus zero in an equation. If you want to find the vertex of this proble, The Vertex is always each comma K. So the ages, this value added at the end, which is three. And then the K is that hidden zero in there. The Vertex is actually three common zero for the axis of symmetry. That's usually the equation y equals K. This is the horizontal line that goes through the proble. So the K value is zero. So why equals zero is the axis of symmetry? No. To find the intercepts will come over here to find the X intercept we're gonna plug in. Why is the road that their definition of a next intercept X equal to time zero squared cost three. So zero Cordish zero times anything is still zero about zero. So I got an X intercept up three and for one intercept, we can do the opposite. We can plug in excess zero. Then we can try and fill this equation speaking. Subtract three on both sides. We get negative. Three equals two I square. We can divide both sides by two. Do we get negative? 1.5 people is like squared and our last step is to take the square root on both sides. But we run into a problem right here because you can't take the square root of a negative number. And since we can't do that, what this tells us is that this proble has no why intersect so visually? What's happening here is that we noticed our X intercept is at 30 which is also the Vertex access. The symmetry is this horizontal exact this and because the a value is positive, this problems opening to the right, so it's never actually gonna cross the y axis. There's no way intercepts and algebraic Lee I figure that out because I got to a point in my equation where I got stuck. We can't figure that out. Okay, So you can overtax with HK our axis of symmetry rifles, K our X intercepts. We plug, dangle I equals zero into our equation on our whiner.


Similar Solved Questions

5 answers
57. The ared function FO) =Vi-ndtan antiderivativefw)=n-r Prove the formulan-7dt = 2 sin ~ 1 X+ i*v1-R+cusing geometry by interpreting the integral as the area of part of the unit circle
57. The ared function FO) = Vi-ndt an antiderivative fw)=n-r Prove the formula n-7dt = 2 sin ~ 1 X+ i*v1-R+c using geometry by interpreting the integral as the area of part of the unit circle...
5 answers
Consider the following Pair of reactions_ Predict the type of substitution mechanism, predict which reaction of the pair will occur at the faster rate and draw the correct organic product;waterSelesanswerwaterSelect snswer
Consider the following Pair of reactions_ Predict the type of substitution mechanism, predict which reaction of the pair will occur at the faster rate and draw the correct organic product; water Selesanswer water Select snswer...
5 answers
If the probabilfyol $ €Ar crossing # {raflic light i P-0.2in one minute what kthe probabilityof crossine ol the 10 cars #roi themime modelin oncminulr
If the probabilfyol $ €Ar crossing # {raflic light i P-0.2in one minute what kthe probabilityof crossine ol the 10 cars #roi themime modelin oncminulr...
5 answers
Question 2-The function f(t) is defined as follows f(t) = =3 6t + €2,0 < t <7 Define f (t), an odd periodic extension of f(t) and hence select the name of the appropriate Fourier half-range series representation of f (t).The Fourier_representation of f (t) is called: SelectEnter the following values in the boxes below: p = f(-5), q = f (11)_ T, the period of f (t).Enter p: Enter q: Enter T:
Question 2- The function f(t) is defined as follows f(t) = =3 6t + €2,0 < t <7 Define f (t), an odd periodic extension of f(t) and hence select the name of the appropriate Fourier half-range series representation of f (t). The Fourier_representation of f (t) is called: Select Enter the f...
5 answers
022 (part 1 of 3) 10.0 points3.1 V2.3 V7.6 V3.2Find the current Ithe 1.7 $2 resistor at the bottom of the circuit betwccn the two power supplies. Answer in units of023 (part 2 of 3) 10.0 points Determine I2. Answer in units of024 (part 3 of 3) 10.0 points Determine I3 Answer in units of
022 (part 1 of 3) 10.0 points 3.1 V 2.3 V 7.6 V 3.2 Find the current I the 1.7 $2 resistor at the bottom of the circuit betwccn the two power supplies. Answer in units of 023 (part 2 of 3) 10.0 points Determine I2. Answer in units of 024 (part 3 of 3) 10.0 points Determine I3 Answer in units of...
4 answers
Find the intcgrating factor that dincrcnutial cquwlion_ A)dr Xtefunction of $ 0T ) Jlonc ind ussfind the general ~olution of IhcPrbkn WLEvaluate the iterated integral:Jcos ydzdrdyFind the Mias: 5 of the lamina described by the inequalities, given that its density is p(x,y) =Xy:0 $xs2,0sYs4-*
Find the intcgrating factor that dincrcnutial cquwlion_ A)dr Xte function of $ 0T ) Jlonc ind uss find the general ~olution of Ihc Prbkn WL Evaluate the iterated integral: J cos ydzdrdy Find the Mias: 5 of the lamina described by the inequalities, given that its density is p(x,y) =Xy: 0 $xs2,0sYs4-*...
5 answers
Wtkch of the folloring feature ot the retrovinuises? belones 0rxTenen trun"Griptasedouble-strnted RNAreQuestion 24Whch schere represents @ class Wwnt{ rure expassion?CetAa(ucn V-nsctiK-D CrHan- (ibud IDFCtTc RIpickurimzLeaona(evct e baneoeiedGDNA whiciTuIRHA{rbldo NnZRaLed @ncthIinthicn kDiala -K RMAEuanc DmkNA Krhlch bandated tD piolcmQuestion 25Wnlch schere rcorcsents clasannb "ent ecnnear?Mjalcbrejok AfR
Wtkch of the folloring feature ot the retrovinuises? belones 0rx Tenen trun"Griptase double-strnted RNA re Question 24 Whch schere represents @ class Wwnt{ rure expassion? CetAa (ucn V-nscti K-D Cr Han- (ibud ID FCtTc RI pickurimz Leaona (evct e baneoeied GDNA whici TuIRHA {rbldo Nn ZRa Led @nc...
5 answers
You stand on weight scale In an elevator that Is accclerating wlth a- -2.5 m/s? (take posl ive upward): If you have mass ot 80 kB what weight does the scale rcad? (In N}4759845847841025
You stand on weight scale In an elevator that Is accclerating wlth a- -2.5 m/s? (take posl ive upward): If you have mass ot 80 kB what weight does the scale rcad? (In N} 475 984 584 784 1025...
5 answers
B) Repeat the test by computing the p-value the test.Construct the 95'7 confidence interval for the population mein . Use it to test Ho against Hi
b) Repeat the test by computing the p-value the test. Construct the 95'7 confidence interval for the population mein . Use it to test Ho against Hi...
5 answers
1,The formal @ges Or Carbon 1 , Carbon 3 aloms mn and Oxigen pxoPamal are(a) (1 =0 C3= 0 0=-1 C1=1 (3=1 0=0 888 C3 1 C1 = C3= 0 2 Predict the direclion this reaction cril go , bagd On the OKa data aS Folqs pKa Hzo 15..75, HCN = 9,31 acetic aad (chc H) 476 nitric aCid (HnOz) -|.3 ; hydroniom ion (Hzo )Ia; ace toe I9.0 ; ammona (Nh3) 36.0__h1 Hcn f @H; Co; Na t Na" N CHSoa H blzsl Q + L 4o R YQ'"xe Wdding rightz be cleterined Fror tke data gien Cannot
1,The formal @ges Or Carbon 1 , Carbon 3 aloms mn and Oxigen pxoPamal are (a) (1 =0 C3= 0 0=-1 C1=1 (3=1 0=0 888 C3 1 C1 = C3= 0 2 Predict the direclion this reaction cril go , bagd On the OKa data aS Folqs pKa Hzo 15..75, HCN = 9,31 acetic aad (chc H) 476 nitric aCid (HnOz) -|.3 ; hydroniom ion (Hz...
5 answers
If you roll a 1 -m-diameter wheel forward 30 cm over level ground, through what angle will the wheel turn? Answer in radians (to the nearest tenth) and degrees (to the nearest degree).
If you roll a 1 -m-diameter wheel forward 30 cm over level ground, through what angle will the wheel turn? Answer in radians (to the nearest tenth) and degrees (to the nearest degree)....
5 answers
Answer (with circle) the following two questions as they relate to a 99% confidence interval for p:a) Is it correct to say that the probability that is in the specified interval is 99%7 Explain.Yes. The probability that H falls inside the interval is 99%.No. The probability that U falls inside the interval is either 0No. The probability that / falls inside the interval is 99%.Yes. The probability that H falls inside the interval is either 0 or 1.
Answer (with circle) the following two questions as they relate to a 99% confidence interval for p: a) Is it correct to say that the probability that is in the specified interval is 99%7 Explain. Yes. The probability that H falls inside the interval is 99%. No. The probability that U falls inside t...
5 answers
What is a structure that is likely to be directalkylation of ammonia (NH3) with(S)-2-bromobutane?
What is a structure that is likely to be direct alkylation of ammonia (NH3) with (S)-2-bromobutane?...
5 answers
1point pisttlnguish thetwo forms of starchAnylaseAmylopectinbranchedlongerminor componentNo Answers ChosenPossible answersmajor componentshonerunbranched
1point pisttlnguish thetwo forms of starch Anylase Amylopectin branched longer minor component No Answers Chosen Possible answers major component shoner unbranched...
5 answers
18, [~/5 Points]DETAILSHARMATHAP1Z 9.3.005.Given fix)4* + find the averaqu to 07 change of Kx) overthe follovring palrsintenval[1.9_ and (1.99, 2] averade change averaye Fale chunac[1,99, 2][2, 2.1] Jnd [?4 01] averaqe changa Ovur [%,2.1] avulaqe fto changa ovt [3,Wnat do tne culculaeloa parts (J) and (b) suggest the Instantaneouschame Kx)mlght be?Need Help?
18, [~/5 Points] DETAILS HARMATHAP1Z 9.3.005. Given fix) 4* + find the averaqu to 07 change of Kx) over the follovring palrs intenval [1.9_ and (1.99, 2] averade change averaye Fale chunac [1,99, 2] [2, 2.1] Jnd [?4 01] averaqe changa Ovur [%,2.1] avulaqe fto changa ovt [3, Wnat do tne culculaeloa p...
5 answers
Population is modeled by the differential equation0.9P 0.0O09P2The population is at equilibrium whenWhen the population is less than the equilibrium population, the population is: decreasing increasing
population is modeled by the differential equation 0.9P 0.0O09P2 The population is at equilibrium when When the population is less than the equilibrium population, the population is: decreasing increasing...

-- 0.021441--