Suppose that g is a quadratic function such that g(x) = 0 only on the interval (-1,7) and g(1)=36.

a. Find the rule of g(x)

b. Find all Valuse of x such that g(x)=10.

c. Find the maximum value of g(x) or explain why no such value exists.

Question

Suppose that g is a quadratic function such that g(x) >= 0 only on the interval (-1,7) and g(1)=36.

a. Find the rule of g(x)

b. Find all Valuse of x such that g(x)=10.

c. Find the maximum value of g(x) or explain why no such value exists.

anonymous · Answer

Since $g$ is quadratic, its general form is$$g(x)=ax^2+bx+c$$
Since $g\ge0$ only on the provided interval, you're essentially told that $g=0$ when $x=-1$ and $x=7$. This means you can factor the above form to look like
$$g(x)=a(x+1)(x-7)$$
Given that $g(1)=36$, you have
$$a(1+1)(1-7)=36~~\iff~~a=-3$$