# Explanation: ## Step1: Identify vertex of parabola The vertex of $y=x^2$ is at $(0,0)$ since it is in the form $y=ax^2+bx+c$ with $b=0, c=0$. ## Step2: Calculate sample points Choose $x$ values, compute $y$: - $x=-3$: $y=(-3)^2=9$ → $(-3,9)$ - $x=-2$: $y=(-2)^2=4$ → $(-2,4)$ - $x=-1$: $y=(-1)^2=1$ → $(-1,1)$ - $x=1$: $y=(1)^2=1$ → $(1,1)$ - $x=2$: $y=(2)^2=4$ → $(2,4)$ - $x=3$: $y=(3)^2=9$ → $(3,9)$ ## Step3: Plot points and draw curve Mark the vertex $(0,0)$ and the sample points, then draw a smooth symmetric parabola through them. # Answer: The graph is a parabola with vertex at $(0,0)$, passing through points $(-3,9), (-2,4), (-1,1), (1,1), (2,4), (3,9)$, opening upward symmetrically across the y-axis.

2. $y = x^2$ | Sovi AI

QUESTION IMAGE

Question

$y = x^2$

Explanation:

Step1: Identify vertex of parabola

The vertex of $y=x^2$ is at $(0,0)$ since it is in the form $y=ax^2+bx+c$ with $b=0, c=0$.

Step2: Calculate sample points

Choose $x$ values, compute $y$:

$x=-3$: $y=(-3)^2=9$ → $(-3,9)$
$x=-2$: $y=(-2)^2=4$ → $(-2,4)$
$x=-1$: $y=(-1)^2=1$ → $(-1,1)$
$x=1$: $y=(1)^2=1$ → $(1,1)$
$x=2$: $y=(2)^2=4$ → $(2,4)$
$x=3$: $y=(3)^2=9$ → $(3,9)$

Step3: Plot points and draw curve

Mark the vertex $(0,0)$ and the sample points, then draw a smooth symmetric parabola through them.

Answer:

The graph is a parabola with vertex at $(0,0)$, passing through points $(-3,9), (-2,4), (-1,1), (1,1), (2,4), (3,9)$, opening upward symmetrically across the y-axis.