Question

The graph of 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. 1/2B. -1/2C. 7/2D. -3/2

Answer 1

A quadratic function can be given as follows:

`f(x)=a(x-x_1)(x-x_2)`

where x1 and x2 are the zeros of the equation, which means that the equation is given by:

`\begin{gathered} f(x)=a(x--8)(x-4)=a(x+8)(x-4) \\ f(x)=a(x^2+4x-32) \end{gathered}`

Because the point (-2, 18) is part of the function, we can substitute it, and isolate a to find its value:

`\begin{gathered} a=(f(x))/(x^2+4x-32)=(18)/((-2)^2+4\cdot(-2)-32)=(18)/(4-8-32)=(18)/(-36)=-(1)/(2) \\ a=-(1)/(2) \end{gathered}`

From the solution developed above, we are able to conclude that the answer for the present problem is:

B. -1/2