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Her Concepts di- x-coordinate the vertex the parabola ea? Find the 4x 12 by averaging the x-coordinates f(x) the y-intercept and its symmetric point x-coordinate th...

Question

Her Concepts di- x-coordinate the vertex the parabola ea? Find the 4x 12 by averaging the x-coordinates f(x) the y-intercept and its symmetric point x-coordinate the vertex the parabola Find the f(x) =x + 4x 12 by averaging the x-coordinates of the x-mntercepts: Compare the methods you used parts (a) and (b)_ Are your results the same" Which method from parts (a) and (b) is easier t0 use find the X-coordinale of the vertex the parabola t0 g(+) 54x2 19Sx 216? Explain. Which method(s) can b

her Concepts di- x-coordinate the vertex the parabola ea? Find the 4x 12 by averaging the x-coordinates f(x) the y-intercept and its symmetric point x-coordinate the vertex the parabola Find the f(x) =x + 4x 12 by averaging the x-coordinates of the x-mntercepts: Compare the methods you used parts (a) and (b)_ Are your results the same" Which method from parts (a) and (b) is easier t0 use find the X-coordinale of the vertex the parabola t0 g(+) 54x2 19Sx 216? Explain. Which method(s) can be used t0 find the x-coordinate of the vertex of the parabola h(x) X2 + 4x 62 Explain. E Summarize your findings in this exercise 70. In this exercise; You will discover how to convert the standard form of a quadratic function to its vertex form;: Find the vertex of the parabola f(x) 3x2 6x + 7. b Recall that if (h, k)is the vertex of the graph of a quadratic function,then f(x) a(x h)? k.Use your result from part (a) to determine h and k for f(x) 3x? 6x + 7. Substitute the values of h and k you found from part (b) in f(x) a(x h)? + k. Compare f(x) 3x2 6x + with your result in part (c): Determine the value of a. [Hint: You may see this immediately If not; write your result in part (c) in stan- dard form and compare again with f(x) 312 6x 7] Substitute your value of a into your result from part (c) 6 Use a graphing calculator to verify your result by comparing the graph of f(x) 3x2 6x with the graph of f(x) 0(35 6)2 + k for the values ofa,h,and k you found



Answers

A parabola associated with a certain quadratic function $f$ has the point (2,8) as its vertex and passes through the point $(4,0) .$ Find an expression for $f(x)$ in the form $f(x)=a(x-h)^{2}+k$ (a) From the given information, find the values of $h$ and $k$ (b) Substitute the values you found for $h$ and $k$ into the expression $f(x)=a(x-h)^{2}+k$ (c) Now find $a$. To do this, use the fact that the parabola passes through the point $(4,0) .$ That is, $f(4)=0$ You should get an equation having just $a$ as a variable. Solve for $a$ (d) Substitute the value you found for $a$ into the expression you found in part (b). (e) Graph the function using a graphing utility and check your answer. Is (2,8) the vertex of the parabola? Does the parabola pass through (4,0)$?$

For this question. We'll use the form off the parabola. Be off. Aches equals a times X minus h the whole spread. Lasky, for this operation here. Given that the vortex is minus X, call on my mistress on it passes to the 0.6 comma 20 full. So minus six is on edge minus. Try and escape. Six eggs on re exist. 20 full for 24 equals P six minus of minus six. The whole square. My mistress, when we simplified us. Well, get the value off eight, which is equal to one upon full. So we put this in the PX Richards. When upon for explosives the whole square. My best friend, we expand on simplifying. Get the function, which is one upon four x squared, less three x Find this study.

We should try the quarter t function X Square, be X plus C is a parable foot part beat. The parable are defined by this will open up what if is good and zero and four down. What is negative. So that means in first of space we should fill this symbol in second of space. We should fill the symbol. See parties. Parable opens of water vortexes friend parable opens a port, the war Texas bluest and when parabola opens downwards. So vortexes highest our deal discussion effects is eight times X minus is hopeless cause in first order, Pierre here is Etch Komaki in second space. We should foot if the parable opens upward. In second case, we should feel a poured in that case, case the minimum and entered space. We should feel downward in that case. Case the maximum value off the Function Party given effects eight times X minus H fully square plus k. The excess of symmetry of the parabola is vertical line that passes through the Etch Go market. So that would pass through that vertical line with passed through H comma K and the question off the line we should write It is X equals toe Etch

In this Grecian. We have been asked to use the form be eggs equals eight times X minus h the holes for Klasky as a hint The vortex given as five, almost six on it passes through the point The parabola one comma minus six. Just 56 pesky one is eggs on minus Experts be Experts are forced Observation. We plug this spend are given function Simplify it toe Find the value off A which gives us the value off eat has minus t a born fool We plug it and opiates to get minus three upon So x minus for you the whole square plus six we expand. I'm simplified this Get our answer in the required form which is minus three upon full X square last 15 apart Do X minus 51 A born fool

For this question, we can use the formula for parabola in this form. React equals G X minus the hospital rescue. We are giving that devote six with minus one comma minus full on the batter Wheeler passes to buy Goma 104 you edge is minus one minus. Full is key. Let's take a point. Why 104 x five by SPX We plug this in the equation above. Find the value of a after simplifying because the value off it as three so the very as the existence to dames X plus one the whole spread minus four, which before the simplified and bypassed three express plus six x minus one.


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