Question

Write the equation for the quadratic function in the graph.

OA) (x) = -1/4(x - 3)(x + 6)
B) h(x) = -1/4(x - 6)(x + 3)
C) h(x) = 1/4(x - 3)(x + 6)
OD) h(x) = 1/4(x - 6)(x + 3)

Answer 1

B) h(x) = -1/4(x - 6)(x + 3)

Explanation:

Zeros of a function:

Given a polynomial f(x), this polynomial has roots
`x_(1), x_(2), x_(n)` such that it can be written as:
`a(x - x_(1))*(x - x_(2))*...*(x-x_n)`, in which a is the leading coefficient.

In this question:

Concave down, so
`a < 0`, which excludes options c and d.

Roots at x = 6 and x = -3. So

`-(1)/(4)(x-6)(x-(-3)) = -(1)/(4)(x-6)(x+3)`

So option B.