Suppose a parabola has an axis of symmetry of $x = -7$, a maximum height of $4$, and passes through point $(-6, 0)$. Write the equation in vertex form.
Here's what I got: $y = -(x + 7)^2 + 4$ The problem is that when I plug in $(-6, 0)$, it doesn't make the equation true. Help.
You are almost there:
Recall that a parabola can satisfy the equation:
$$y = A(x-h)^2 + k$$
We can alter the value of $A$ to satisfy the condition for amplitude.
$$y = A(x+7)^2 + 4$$
Since it passes through the point $(-6,0)$
$$0 = A(1)^2 + 4,\ A = -4$$
Therefore, the equation is:
$$y = -4(x+7)^2 + 4$$
