How do you find two quadratic function one that opens up and one that opens downward whose graphs have intercepts (-5,0), (5,0)?

1 Answer
Noah G
Jan 7, 2017

Many answers possible:
Ex. #y = 2x^2 - 50# opens up and #y = -24x^2 + 600# opens down

Explanation:

The form #y = c(x - a)(x - b)# represents intercept form, where #c# is a constant. If #c > 0#, the parabola opens up. If #c < 0#, the parabola opens down.

So, we can pick absolutely any value of #c# that is below #0# if we want the parabola to open down and absolutely any value of #c# that is above #0# if we want the parabola to open up.

Thus, we can have equations:

#y = 2(x - 5)(x + 5)#
#y = 2(x^2 - 25)#
#y = 2x^2 - 50# opens up

AND

#y = -24(x -5)(x + 5)#
#y = -24(x^2 - 25)#
#y = -24x^2 + 600# opens downwards

Hopefully this helps!

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