Question

question
graph the equation shown below by transforming the given graph of the parent function.
$y = x^2 - 2$

Explanation:

Step1: Identify parent function

The parent function is $y=x^2$, with vertex at $(0,0)$.

Step2: Recognize transformation type

$y=x^2-2$ is a vertical shift down by 2 units.

Step3: Transform key points

For each point $(x, x^2)$ on $y=x^2$, new point is $(x, x^2-2)$:

• $(0,0) \to (0, 0-2)=(0,-2)$
• $(1,1) \to (1, 1-2)=(1,-1)$
• $(-1,1) \to (-1, 1-2)=(-1,-1)$
• $(2,4) \to (2, 4-2)=(2,2)$
• $(-2,4) \to (-2, 4-2)=(-2,2)$
• $(3,9) \to (3, 9-2)=(3,7)$
• $(-3,9) \to (-3, 9-2)=(-3,7)$

Step4: Plot and connect points

Draw a parabola through the transformed points.

Answer:

The graph of $y=x^2-2$ is a parabola with vertex at $(0,-2)$, shifted 2 units downward from the parent parabola $y=x^2$, passing through points like $(\pm1,-1)$, $(\pm2,2)$, and $(\pm3,7)$.