Question

when the solutions to each of the two equations below are graphed in the xy-coordinate plane, the graphs intersect at two places. Write the y-coordinates of the points of intersection in the boxes below in order from smallest to largest

y=2x

y+x^2 - 3

Answer 1

The answer is -2 and 6

Answer 2

Intersection points (1,2) and (-3,-6)

The y-coordinates of the points of intersection from smallest to largest is -6 to 2.

Explanation:

Given : A system of equations
`y=2x` and
`y+x^2 - 3=0`

To find : Write the y-coordinates of the points of intersection?

Solution :

Let,
`y_1=2x`

and
`y_2=3-x^2`

Now, we plot these two equations.

The graph of
`y_1=2x` is shown with red line.

The graph of
`y_2=3-x^2` is shown with blue line.

The solution to this system will be their intersection point.

The intersection points of these graph are (1,2) and (-3,-6).

Refer the attached graph below.

Therefore, The y-coordinates of the points of intersection from smallest to largest is -6 to 2.