c They are mirror images of each other in the x-axis.
D
d x≈ -2.2 and x≈ 2.2
E
e x≈ -3.2 and x≈ 3.2
Practice makes perfect
a Let's first make the table by putting in some value of x into the given equation.
|c|c|c|
[-1em]
x & x^2 & y [0.2em]
[-1em]
-2 & ( -2)^2 & 4 [0.2em]
[-1em]
-1 & ( -1)^2 & 1 [0.2em]
[-1em]
0 & 0^2 & 0 [0.2em]
[-1em]
1 & 1^2 & 1 [0.2em]
[-1em]
2 & 2^2 & 4 [0.2em]
When we know a few points through which the functions passes, we can graph the function.
b Let's first make the table.
|c|c|c|
[-1em]
x & - x^2 & y [0.2em]
[-1em]
-2 & -( -2)^2 & - 4 [0.2em]
[-1em]
-1 & -( -1)^2 & -1 [0.2em]
[-1em]
0 & - 0^2 & 0 [0.2em]
[-1em]
1 & - 1^2 & -1 [0.2em]
[-1em]
2 & - 2^2 & -4 [0.2em]
When we know a few points through which the functions passes, we can graph the function.
c Let's put the graphs in the same coordinate plane so we can compare them more easily.
If we compare a few points on the graphs that lie on the same x-coordinate, we notice that the segments between them are equidistant from and perpendicular to the x-axis.
As we can see, the two graphs are mirror images of each other in the x-axis.
d To estimate the x-values when y=5, we should draw y=5 in the coordinate plane from Part A and determine where the two two functions intersect.
As we can see, the x-values corresponding to y=5 is x≈ -2.2 and x≈ 2.2.
e To estimate the x-values when y=-10, we should draw y=-10 in the coordinate plane from Part B and determine where the two functions intersect.
As we can see, the x-values corresponding to y=-10 is x≈ -3.2 and x≈ 3.2.
