Which equation represents the function shown in the graph?
Check the final answer first, then review the worked steps.
Problem
Which equation represents the function shown in the graph?
Step-by-step solution
The graph shows a parabola with x-intercepts at (-4, 0) and (-2, 0). The vertex is at (-3, -6). The factored form of the quadratic is $f(x) = a(x+4)(x+2)$. Using the vertex, $-6 = a(-3+4)(-3+2) = a(1)(-1) = -a$, so $a=6$. Expanding, $f(x) = 6(x^2 + 6x + 8) = 6x^2 + 36x + 48$.
Answer
D