Question

consider the quadratic function written below in intercept form. f(x) = (x - 2)(x - 4) which of the following represents the vertex of the quadratic function? a (2, 0) b (3, 0) c (4, 0) d (2, 4) e (3, -1)

Explanation:

Step1: Find the x - coordinate of the vertex

For a quadratic function in intercept form \(f(x)=(x - p)(x - q)\), the x - coordinate of the vertex (the axis of symmetry) is given by \(x=\frac{p + q}{2}\). Here, \(p = 2\) and \(q = 4\), so \(x=\frac{2 + 4}{2}=\frac{6}{2}=3\).

Step2: Find the y - coordinate of the vertex

Substitute \(x = 3\) into the function \(f(x)=(x - 2)(x - 4)\). Then \(f(3)=(3 - 2)(3 - 4)=(1)\times(- 1)=-1\). So the vertex is \((3,-1)\).

Answer:

E. (3, -1)