Question

What is the equation of the function represented by this graph?

Answer 1

`\displaystyle g(x) = -(x + 2)(x - 4)`

Explanation:

First, look at the graph to determine whether it opens down or up, which in this case is down, so you insert a negative in front of the expression. Next, locate your x-intercepts [zeros (where the graph insects the x-axis)]. You will see that the graph intersects
`\displaystyle [-2, 0]` and
`\displaystyle [4, 0],` so what you do is insert the zeros' OPPOCITES into the equation because according to the vertex equation,
`\displaystyle y = A[x - h]^2 + k,` that negative in front of
`\displaystyle h` gives you the OPPOCITE outcome, so be careful.

I am joyous to assist you at any time.