Question

What must be a factor of the polynomial function f(x) graphed on the coordinate plane below? On a coordinate plane, a parabola opens up. It goes through (0, 3), has a vertex at (3.5, 3), and goes through (6, 0). x – 3 x – 1 x + 1 x + 3 Mark this and return

Answer 1

The axis of symmetry of the parabola is the vertical line passing through the vertex, which is x = 3.5. Since the parabola is symmetric about this line, its roots (or zeros) must be equidistant from the axis of symmetry.

The distance between the axis of symmetry x = 3.5 and the point (0, 3) is 3.5, so the distance between the axis of symmetry and the other x-intercept must also be 3.5. This other x-intercept is (6, 0), so the distance between x = 3.5 and x = 6 is 2.5.

Therefore, the roots of the polynomial function are x = 3.5 - 2.5 = 1 and x = 3.5 + 2.5 = 6, which means that the factors of the polynomial are (x - 1) and (x - 6).

So, the answer is x - 1 or (x - 1)