## 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