sketch the graph of the function. g(x)=(x + 8)^2 use the graphing tool to graph the function.

Explanation:

Step1: Identify the vertex - form of parabola

The general vertex - form of a parabola is $y=a(x - h)^2+k$, where $(h,k)$ is the vertex. For the function $g(x)=(x + 8)^2=(x-(-8))^2+0$, the vertex is $(-8,0)$ and $a = 1>0$, so the parabola opens upwards.

Step2: Find the y - intercept

Set $x = 0$. Then $g(0)=(0 + 8)^2=64$. So the y - intercept is $(0,64)$.

Step3: Find the x - intercept

Set $g(x)=0$. Then $(x + 8)^2=0$, which gives $x=-8$. So the x - intercept is $(-8,0)$.

Step4: Plot key points and draw the graph

Plot the vertex $(-8,0)$, the y - intercept $(0,64)$. Since the parabola is symmetric about the vertical line $x=-8$, we can use the symmetry to find more points if needed and then draw a smooth curve to form the parabola.

Answer:

To graph the function $g(x)=(x + 8)^2$, plot the vertex at $(-8,0)$, the y - intercept at $(0,64)$ and draw an upward - opening parabola symmetric about the line $x=-8$.