Question

Find a formula for the quadratic function whose graph has a vertex at(7,2) and zeros at x = -1 and x = 15.NOTE: Enter the exact answer.y =

Answer 1

General form y= ax^2+bx+c

standard form y = a(x-h)^2+k

where

(h,k)= vertex = (7,2)

Since the zero are at -1 and 15 we have the points

(-1,0) and (15,0)

We will use one of the points (-1,0) and the vertex in the general form:

0= a(-1-7)^2+2

0= a(-8)^2+2

0= a64+2

-2 =a64

-2/64 =a

-1/32 =a

y= -1/32 (x-7)^2+2

y =-1/32 (x-7)(x-7)+2

y= -1/32 (x^2-14x+49)+2

y= -1/32 x^2+7/16x-49/32+2

y= -1/32x^2+7/16x-113/32