Question

graph the function f(x) = -3(x + 5)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 \( f(x) = -3(x + 5)^2 \) 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 \( k = 0 \), so the vertex is \( (-5, 0) \).

Step2: Find another point

Let's choose \( x = -4 \) (a value close to the vertex). Substitute \( x = -4 \) into the function: \( f(-4) = -3(-4 + 5)^2 = -3(1)^2 = -3 \). So the point \( (-4, -3) \) is on the parabola. (We can also choose other \( x \)-values, like \( x = -6 \), which gives \( f(-6) = -3(-6 + 5)^2 = -3(-1)^2 = -3 \), so \( (-6, -3) \) is also on the parabola.)

Step3: Graph the vertex and point

Plot the vertex \( (-5, 0) \) on the coordinate plane. Then plot the point \( (-4, -3) \) (or \( (-6, -3) \)). Since \( a = -3 < 0 \), the parabola opens downward.

Answer:

The vertex is at \( (-5, 0) \), and another point (e.g., \( (-4, -3) \) or \( (-6, -3) \)) can be plotted to graph the parabola.