Question

graph the function f(x) = -5(x + 1)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 \( f(x) = -5(x + 1)^2 + 2 \) is in vertex form \( f(x)=a(x - h)^2 + k \), where the vertex is \( (h,k) \). Here, \( h=-1 \) (since \( x+1=x - (-1) \)) and \( k = 2 \). So the vertex is \( (-1,2) \).

Step2: Find another point

Let's choose \( x = 0 \) to find a point. Substitute \( x = 0 \) into the function: \( f(0)=-5(0 + 1)^2+2=-5(1)+2=-5 + 2=-3 \). So the point \( (0,-3) \) is on the parabola.

Step3: Plot the points

First, plot the vertex \( (-1,2) \) on the graph. Then plot the point \( (0,-3) \). The parabola opens downward because \( a=-5<0 \), and we can sketch the parabola through these points.

Answer:

Vertex: \((-1, 2)\), Another point: \((0, -3)\) (plot these on the given grid)