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Find a formula for a quadratic function whose graph has x-intercepts at (1, 0) and (5, 0), and y-intercept at (0, 7).

 Feb 8, 2021
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The x-intercepts are at (1, 0) and (5, 0). This means the roots of the quadratic function are 1 and 5.

 

We can be sure that the quadratic function is of the form \(f(x) = C (x - 1)(x - 5)\) where C is a constant.

 

We can substitute the point (x, f(x)) = (0, 7) into the equation to find C.

 

7 = C (-1)(-5)

C = 7/5.

 

Therefore \(f(x) = \dfrac 75 (x - 1)(x - 5)\)

 Feb 8, 2021

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