Question

Which system of equations is represented by the graph?

one parabola opening upwards and one parabola opening downwards intersecting at points (3, 9) and (-3, 9)

y = x2 + 3x

y = –x2 + x + 18
y = x2

y = –x2 +18
y = x2

y = x2 + 18
y = x2

y = –x2 – x – 18

Answer 1

y = x2

y = –x2 +18

Explanation:

I got it right on the test.

Answer 2

Blue: y = x²

Red: y = -x² + 18

Explanation:

The blue parabola opens upwards, therefore the term in x² is positive.

The red parabola opens downwards, therefore the term in x² is negative.

The x-value of the vertices of both parabolas is x = 0.

Therefore, the equations of both parabolas will not have a term in x.

The y-intercept of the blue parabola is also the y-value its vertex: y = 0.

The y-intercept of the red parabola is also the y-value its vertex: y = 18.

Therefore, the equation for each parabola is:

• Blue: y = x²
• Red: y = -x² + 18

To check, substitute x = ±3 into both equations:

Blue

`x=3 \implies y=(3)^2=9`

`x=-3 \implies y=(-3)^2=9`

Red

`x=3 \implies y=-(3)^2+18=9`

`x=-3 \implies y=-(-3)^2+18=9`