Question

graph the function f(x) = -3(x + 9)² + 8. 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 vertex form

The function \( f(x) = -3(x + 9)^2 + 8 \) is in vertex form \( f(x) = a(x - h)^2 + k \), where vertex is \( (h, k) \). Here, \( h = -9 \) (since \( x + 9 = x - (-9) \)) and \( k = 8 \). So vertex is \( (-9, 8) \).

Step2: Find another point

Choose \( x = -8 \) (close to \( x = -9 \) for simplicity). Substitute into \( f(x) \):
\( f(-8) = -3(-8 + 9)^2 + 8 = -3(1)^2 + 8 = -3 + 8 = 5 \). So point \( (-8, 5) \) is on the parabola.

Step3: Plot points

Plot vertex \( (-9, 8) \) and point \( (-8, 5) \) (or other valid point) on the graph. The parabola opens downward (since \( a = -3 < 0 \)) with vertex at \( (-9, 8) \) and passes through \( (-8, 5) \) (or similar).

Answer:

Vertex: \((-9, 8)\); Another point (e.g., \((-8, 5)\)) plotted on the parabola.