Question

graph the function $f(x) = -4(x + 3)^{2} + 2$. 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 \( f(x) = -4(x + 3)^2 + 2 \) is in vertex form \( f(x) = a(x - h)^2 + k \), where the vertex is \( (h, k) \). Here, \( h = -3 \) (since it's \( x + 3 = x - (-3) \)) and \( k = 2 \), so the vertex is \( (-3, 2) \).

Step2: Find another point

Let's choose \( x = -2 \) (a value close to the vertex for simplicity). Substitute \( x = -2 \) into the function:
\( f(-2) = -4(-2 + 3)^2 + 2 = -4(1)^2 + 2 = -4 + 2 = -2 \). So the point \( (-2, -2) \) is on the parabola.

Answer:

Vertex: \((-3, 2)\), Another point: \((-2, -2)\) (plot these points on the graph to sketch the parabola)