Question

graph the parabola.
y = -3(x + 4)^2 - 1
plot five points on the parabola: the vertex, two points to the left of the button.

Explanation:

Step1: Find the vertex

The vertex - form of a parabola is $y = a(x - h)^2+k$, where $(h,k)$ is the vertex. For $y=-3(x + 4)^2-1$, $h=-4$ and $k = - 1$. So the vertex is $(-4,-1)$.

Step2: Choose $x$ - values to the left of the vertex

Let $x=-5$. Then $y=-3(-5 + 4)^2-1=-3\times(-1)^2-1=-3 - 1=-4$. The point is $(-5,-4)$.

Step3: Choose another $x$ - value to the left of the vertex

Let $x=-6$. Then $y=-3(-6 + 4)^2-1=-3\times(-2)^2-1=-3\times4-1=-12 - 1=-13$. The point is $(-6,-13)$.

Step4: Choose $x$ - values to the right of the vertex

Let $x=-3$. Then $y=-3(-3 + 4)^2-1=-3\times1^2-1=-3 - 1=-4$. The point is $(-3,-4)$.

Step5: Choose another $x$ - value to the right of the vertex

Let $x=-2$. Then $y=-3(-2 + 4)^2-1=-3\times2^2-1=-3\times4-1=-12 - 1=-13$. The point is $(-2,-13)$.

Answer:

The five points are $(-4,-1),(-5,-4),(-6,-13),(-3,-4),(-2,-13)$