Equations are used to represent the relationships between variables. In [tex]y=x^2 -1[/tex], the variables are x & y and the following observations are true for the given equation:
- The words that describe [tex]y=x^2 -1[/tex] are: y is 1 less than the square of x
- The values of a and b are 3 and 0, respectively.
Given that:
[tex]y=x^2 -1[/tex]
[tex]x^2 \to[/tex] the square of x
So, means that: the y is 1 less than the square of x
From the attached table, we have:
[tex]x = -2; y = a[/tex]
This means that:
[tex]a = (-2)^2 - 1[/tex]
[tex]a = 4 - 1[/tex]
[tex]a =3[/tex]
Also, we have:
[tex]x = b; y = -1[/tex]
This means that:
[tex]-1 = b^2 - 1[/tex]
Collect like terms
[tex]b^2 =1-1[/tex]
[tex]b^2 =0[/tex]
Take square roots
[tex]b = 0[/tex]
Hence, the values of a and b are 3 and 0, respectively.
The graph options are not made available. So, I will plot the graph of [tex]y=x^2 -1[/tex].
See attachment for graph of [tex]y=x^2 -1[/tex]
Read more about graphs and equations at:
https://brainly.com/question/1971145
