Answer:
Part 1) The y-intercept is the point [tex](0,-3)[/tex]
Part 2) The x-intercepts are the points [tex](-\sqrt{3},0)\ and\ (\sqrt{3},0)[/tex]
Step-by-step explanation:
we have
[tex]y=x^{2}-3[/tex]
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
[tex]y=(0)^{2}-3[/tex]
[tex]y=-3[/tex]
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
[tex]x^{2}-3=0[/tex]
solve for x
Adds 3 both sides
[tex]x^{2}-3+3=0+3[/tex]
[tex]x^{2}=3[/tex]
take square root both sides
[tex]x=(+/-)\sqrt{3}[/tex]
so
The x-intercepts are the points [tex](-\sqrt{3},0)\ and\ (\sqrt{3},0)[/tex]
