Question

graph the function $f(x) = 8(x - 6)^2 - 1$. 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 is given in vertex form \( f(x) = a(x - h)^2 + k \), where \((h, k)\) is the vertex. For \( f(x) = 8(x - 6)^2 - 1 \), we have \( h = 6 \) and \( k = -1 \). So the vertex is \((6, -1)\).

Step2: Find another point

Let's choose \( x = 7 \). Substitute \( x = 7 \) into the function: \( f(7) = 8(7 - 6)^2 - 1 = 8(1)^2 - 1 = 8 - 1 = 7 \). So the point \((7, 7)\) is on the parabola.

Step3: Plot the points

First, plot the vertex \((6, -1)\) on the graph. Then plot the point \((7, 7)\). The parabola opens upward because \( a = 8 > 0 \), and we can sketch the parabola using these points.

Answer:

The vertex is \((6, -1)\) and another point is \((7, 7)\) (or other valid point, e.g., \( x = 5 \) gives \( f(5) = 8(5 - 6)^2 - 1 = 8 - 1 = 7 \), so \((5, 7)\) is also valid). When graphing, plot \((6, -1)\) and one of these points, then draw the upward - opening parabola.