Find a formula for a quadratic function whose graph has x-intercepts at (1, 0) and (5, 0), and y-intercept at (0, 7).
+9519 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 \(f(x) = \dfrac 75 (x - 1)(x - 5)\)
