Question

graph the function $f(x) = -7(x + 4)^2 + \frac{3}{2}$. 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 vertex form

The function \( f(x) = -7(x + 4)^2 + \frac{3}{2} \) is in vertex form \( f(x) = a(x - h)^2 + k \), where vertex is \( (h, k) \). Here, \( h = -4 \), \( k = \frac{3}{2} \) (since \( x + 4 = x - (-4) \)). So vertex is \( (-4, \frac{3}{2}) \) (or \( (-4, 1.5) \)).

Step2: Find another point

Choose \( x = -3 \) (one unit right of vertex's x - coordinate). Substitute into \( f(x) \):
\( f(-3) = -7(-3 + 4)^2 + \frac{3}{2} = -7(1)^2 + \frac{3}{2} = -7 + 1.5 = -5.5 \). So point is \( (-3, -5.5) \).

Step3: Plot points

Plot vertex \( (-4, 1.5) \) and \( (-3, -5.5) \) on the grid. The parabola opens downward (since \( a = -7 < 0 \)).

Answer:

Vertex: \((-4, \frac{3}{2})\), Another point: \((-3, -\frac{11}{2})\) (or plotted on the graph as described)