Algebra 2 question

Question

The quadratic function g(x) = (x+3)^2 - 2is given below. The function h(x) is a transformation of g(x). Write an equation for h(x) in terms of g(x).

(x, g(x)) values are (-4,-1), (-3,-2), (-2,-1), (-1,2), (0,7)

(x, h(x)) values are (0,2), (1,1), (2,2), (3,5), (4,10)

Answer 1

If you're having trouble finding the vertex of h, try plotting the points, it should reveal itself!

Answer 2

Look for one of the points being a vertex (highest/lowest point) of the parabola based on the given data.

For g(x), the vertex is (-3, -2).

For h(x), the vertex is (1, 1).

h(x) = [(x + 3) - 4]² + (-2 + 3) = (x + 3 - 4)² + (-1) = (x - 1)² + 1

From g(x), you translate 4 units to the right and 3 units upward.