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?​

Answer 1

Answer:  The value of a is 0.

Quadratic function: A function is said to be quadratic if it takes the form x$f(x) = ax^2 + bx + c,$where a, b, and c are numbers and an is not equal to zero in any of the expressions.

Step-by-step explanation:

Step 1: Given

Let the roots be

$x_1 = -8\\x_2 = 4$

The function is quadratic therefore $f = y = ax^2+bx+c$

Minimum at $x = -2 \\y = 18$

Step 2:

Substituting $x_1$ in y

$64a - 8b=-c-----1$

substituting $x_2$ in y

$16a+4b = -c-----2$

Minimum of f

$\frac{df}{dx}=0$

$2ax+b = 0-----3\\at\hspace{12}x = -2\\b = -4a-----4$

Step 3: Substituting equation 4 in equation 2

$16a + 4(-4a) = -c\\16a - 16a = -c\\therefore \hspace{5} c = 0-----5$

Substituting equation 5 and 4 in 1 we get

a = 0

Therefore a = 0

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