Answered

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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

Sagot :

A quadratic function can be given as follows:

[tex]f(x)=a(x-x_1)(x-x_2)[/tex]

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

[tex]\begin{gathered} f(x)=a(x--8)(x-4)=a(x+8)(x-4) \\ f(x)=a(x^2+4x-32) \end{gathered}[/tex]

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

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

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

B. -1/2

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