help me !!!!!!

Question

The vertex of a parabola that opens downward is at (0, 4). The vertex of a second parabola is at (0, –4). If the parabolas intersect at two points, which statement must be true?

Answer 1

If the first parabola is downward at (0, 4) it could intersect another parabola at (0. -4) if

1) the second parabola opens upward, or

2) if the leading coefficient of the first parabola was sufficiently greater (thinner) than the leading coefficient of the second (flattened).

Answer 2

Hi Myasia.

 

One possible option for the problem you describe is to write the equation for each parabola.

 

y₁ = 4 - x^{2   (the one opening down with vertex at (0, 4)}

 

y₂ = x² - 4   ( the one opening up with the vertex at (0, -4)

 

Since these two parabolas intersect at two points, these two points would be where the two graphs have the same x- and y-values.

 

Set the y₁ = y₂  and find the x's you need.

 

4 - x² = x² + 4

 

Subtract 4 from both sides

 

-x² = x²

 

add x² to both sides

 

0 = 2x²

 

In this case, both x's are 0.

Plug "0" back into the original equations to find the y's

 

Two points of intersection are (0, -4)  and  (0,4)

 

 

Was this one of your choices?