Question

X-intercept and y-intercepts og y=x^2-3

Answer 1

Answer:

Part 1) The y-intercept is the point $(0,-3)$

Part 2) The x-intercepts are the points $(-\sqrt{3},0)\ and\ (\sqrt{3},0)$

Step-by-step explanation:

we have

$y=x^{2}-3$

This is a vertical parabola open upward

step 1

Find the y-intercept

we know that

The y-intercept is the value of y when the value of x is equal to zero

so

For x=0

$y=(0)^{2}-3$

$y=-3$

The y-intercept is the point (0,-3)

step 2

Find the x-intercepts

we know that

The x-intercept is the value of x when the value of y is equal to zero

so

For y=0

$x^{2}-3=0$

solve for x

Adds 3 both sides

$x^{2}-3+3=0+3$

$x^{2}=3$

take square root both sides

$x=(+/-)\sqrt{3}$

so

The x-intercepts are the points $(-\sqrt{3},0)\ and\ (\sqrt{3},0)$