Question

1. use the equation y = 4(x + 5)^2 - 7 to answer the following questions.

a. state the vertex (_, _)
b. state the a value _
circle one: stretch or compress
circle one: opens up or down
c. graph

Explanation:

Step1: Recall vertex - form of a parabola

The vertex - form of a parabola is $y=a(x - h)^2+k$, where $(h,k)$ is the vertex. For the equation $y = 4(x + 5)^2-7$, we can rewrite it as $y=4(x-(- 5))^2+(-7)$. So the vertex is $(-5,-7)$.

Step2: Identify the value of a

In the equation $y = 4(x + 5)^2-7$, the value of $a$ is $4$. Since $a = 4>0$, the parabola stretches (because $|a|>1$) and opens up.

Step3: Graph the parabola

1. Plot the vertex at the point $(-5,-7)$.
2. Since $a = 4$, we can find a few more points. Let $x=-4$, then $y=4(-4 + 5)^2-7=4\times1^2-7=4 - 7=-3$. Let $x=-6$, then $y=4(-6 + 5)^2-7=4\times(-1)^2-7=4 - 7=-3$. We can find more points in a similar way and then connect them with a smooth curve to get the graph of the parabola.

Answer:

a. $(-5,-7)$
b. $a = 4$, stretch, opens up
c. Plot vertex at $(-5,-7)$ and additional points based on the equation and connect with a smooth curve.