The graph of a quadratic function f has zeros of -8 and 4 and a maximum at (-2,18). What is the value of a in the function’s equation?
A) 7/2
B) -3/2
C) -1/2
D) 1/2

Work Shown:

We will use the general vertex form y = a(x-h)^2+k

(h,k) is the vertex, and the 'a' value stretches or compresses the graph vertically

(h,k) = (-2,18) since the highest point is at (-2,18)

Use either root -8 or 4 to plug into the equation as well. I'll use -8

The root -8 means the point (-8,0) is an x intercept.

Plug the values mentioned into the equation below. Then solve for 'a'.

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

y = a(x-(-2))^2+18 ... plug in (h,k) = (-2,18)

y = a(x+2)^2+18

0 = a(-8+2)^2+18 ... plug in (x,y) = (-8,0)

0 = a(-6)^2+18

0 = a*36+18

0 = 36a+18

36a+18 = 0

36a = -18 ... subtract 18 from both sides

a = -18/36 divide both sides by 36

a = (-1*18)/(2*18)

Alternatively, you could use (x,y) = (4,0), instead of (x,y) = (-8,0), and you'll get the same 'a' value as well.  

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step-by-step explanation: