Question

A quadratic function y = f(x) is plotted

on a graph and the vertex of the resulting parabola is (6, -3). What is the vertex of the function defined as
q(x) = f(x +3) +5?

Answer 1

Explanation:

To find the vertex of the function q(x) = f(x + 3) + 5, we need to shift the vertex of the original function f(x) by (3, 5).

Given that the vertex of f(x) is (6, -3), we can apply the shift to find the new vertex of q(x).

The x-coordinate of the new vertex is obtained by subtracting 3 from the x-coordinate of the original vertex:

x-coordinate of q(x) = 6 - 3 = 3

The y-coordinate of the new vertex is obtained by adding 5 to the y-coordinate of the original vertex:

y-coordinate of q(x) = -3 + 5 = 2

Therefore, the vertex of the function q(x) = f(x + 3) + 5 is (3, 2).