Answer:
[tex]\displaystyle g(x) = -(x + 2)(x - 4)[/tex]
Step-by-step 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 [tex]\displaystyle [-2, 0][/tex] and [tex]\displaystyle [4, 0],[/tex] so what you do is insert the zeros' OPPOCITES into the equation because according to the vertex equation, [tex]\displaystyle y = A[x - h]^2 + k,[/tex] that negative in front of [tex]\displaystyle h[/tex] gives you the OPPOCITE outcome, so be careful.
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