Question

graph the function $f(x)=x^2 - 2$. then use the line tool to draw the line $x = 2$ and then use the dot tool to plot the point $(2,f(2))$.

Explanation:

Step1: Find vertex of $f(x)$

The function $f(x)=x^2-2$ is a parabola in the form $f(x)=x^2+k$, with vertex at $(0, -2)$.

Step2: Calculate $f(2)$

Substitute $x=2$ into the function:
$f(2)=2^2 - 2 = 4 - 2 = 2$
So the point is $(2, 2)$.

Step3: Graph the parabola

Plot the vertex $(0,-2)$, and additional points (e.g., $(-1,-1), (1,-1), (-2,2), (2,2)$), then draw a smooth upward-opening parabola through them.

Step4: Plot the point $(2,f(2))$

Mark the point $(2, 2)$ on the graph.

Answer:

1. The graph of $f(x)=x^2-2$ is an upward-opening parabola with vertex at $(0, -2)$, passing through points like $(-1,-1)$, $(1,-1)$, $(-2,2)$, $(2,2)$.
2. The plotted point is $(2, 2)$.