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

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

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Answer 1 · 2017-01-07T15:22:59

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

Explanation:

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

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

Thus, we can have equations:

$y = 2 (x - 5) (x + 5)$ $y = 2(x - 5)(x + 5)$
$y = 2 (x^{2} - 25)$ $y = 2(x^2 - 25)$
$y = 2 x^{2} - 50$ $y = 2x^2 - 50$ opens up

AND

$y = - 24 (x - 5) (x + 5)$ $y = -24(x -5)(x + 5)$
$y = - 24 (x^{2} - 25)$ $y = -24(x^2 - 25)$
$y = - 24 x^{2} + 600$ $y = -24x^2 + 600$ opens downwards

Hopefully this helps!

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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

Explanation:

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