By using the roots and the given point, we conclude that the quadratic equation is:
y = 5*(x - 5)*(x - 9).
We know that if a quadratic has a leading coefficient a, and the roots x₁ and x₂, we can write it as:
y = a*(x - x₁)*(x - x₂).
In this case, we know that it passes through the points (5, 0) and (9, 0), then we conclude that the quadratic equation is:
y = a*(x - 5)*(x - 9).
Now, we also know that the equation passes through (7, - 20), then we have that:
-20 = a*(7 - 5)*(7 - 9)
-20 = a*(2)*(-2) = a*-4
-20/-4 = a = 5
The quadratic equation is:
y = 5*(x - 5)*(x - 9)
If you want to learn more about quadratic equations, you can read:
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