Question

Give the vertex form and factored form of the function f(x) = x^2 - 15x. What specific information does each form provide?

A) Vertex form: f(x) = (x - 7.5)^2 - 56.25; Factored form: f(x) = x(x - 15)
B) Vertex form: f(x) = x^2 - 15x + 56.25; Factored form: f(x) = (x - 7.5)(x - 7.5)
C) Vertex form: f(x) = x^2 - 15x + 56.25; Factored form: f(x) = x(x - 15)
D) Vertex form: f(x) = (x - 7.5)^2 - 56.25; Factored form: f(x) = (x - 7.5)(x - 7.5)

Answer 1

The vertex form of the function f(x) = x^2 - 15x is f(x) = (x - 7.5)^2 - 56.25. The factored form of the function is f(x) = x(x - 15). The vertex form provides information about the vertex of the parabola, while the factored form shows the zeros of the function.

Step-by-step explanation:

The vertex form of the function f(x) = x^2 - 15x is f(x) = (x - 7.5)^2 - 56.25. The factored form of the function is f(x) = x(x - 15).

The vertex form provides information about the vertex of the parabola, which is (7.5, -56.25). It tells us that the parabola opens upwards and is at its minimum value at the vertex.

The factored form shows the zeros of the function, which are x = 0 and x = 15.

These are the points where the graph of the function intersects the x-axis.