Question

graph the function f(x) = 8(x + 5)² - 7. plot the vertex. then plot another point on the parabola. if you make a mistake, you can erase your parabola by selecting the second point and placing it on top of the first.

Explanation:

Step1: Identify the vertex form

The function \( f(x) = 8(x + 5)^2 - 7 \) is in vertex form \( f(x) = a(x - h)^2 + k \), where the vertex is \( (h, k) \). Here, \( h = -5 \) (since \( x + 5 = x - (-5) \)) and \( k = -7 \). So the vertex is \( (-5, -7) \).

Step2: Find another point

Let's choose \( x = -4 \) (a value close to the vertex for simplicity). Substitute \( x = -4 \) into the function:
\( f(-4) = 8(-4 + 5)^2 - 7 = 8(1)^2 - 7 = 8 - 7 = 1 \). So the point \( (-4, 1) \) is on the parabola.

Step3: Plot the points

First, plot the vertex \( (-5, -7) \) on the graph. Then plot the point \( (-4, 1) \). The parabola opens upward because \( a = 8 > 0 \), so we can sketch the parabola using these two points (and symmetry if needed).

Answer:

Vertex: \((-5, -7)\), Another point: \((-4, 1)\) (plot these on the given grid to graph the parabola)