Find two quadratic funcitons one that opens upward and one t

Find two quadratic funcitons, one that opens upward and one that opens downward, whose graphs have the given x-intercepts. (4,0), (8,0)

Solution

(4,0), (8,0)

These are the zeros (x-intercepts)

So, we have factors (x-4)(x-8)

Multipy it out :

f(x) = x^2 - 12x + 32 ---> opens upward

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Downward :

Simply negate the one above

g(x) = -(x^2 - 12x + 32)

g(x) = -x^2 + 12x - 32 ---> opens downward as the x^2 term is with a negative coefficient

Hope this made sense!

Cheers!