How do you find two quadratic function one that opens up and one that opens downward whose graphs have intercepts (-1,0), (3,0)?

Question

18703 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-12-31T15:40:22

Please see the explanation.

Because the quadratic function is zero, when #x = -1 and x = 3#, it will have the factors:

#y = k(x + 1)(x - 3)#

where k is an unknown constant that one can use to force the quadratic to pass through a point with a non-zero y coordinate.

If #k > 0#, then the quadratic opens upward.

If #k < 0#, then the quadratic opens downward.

I will multiply the factors:

#y = k(x^2 -2x - 3)#

I will chose #k = 1#

#y = x^2 -2x - 3" [1]"#

Now I will choose #k = -1#

#y = -x^2 +2x + 3" [2]"#

Equation [1] opens upward and equation [2] opens downward; both have the same intercepts, #(-1,0) and (3,0)#