The transformation that converts the graph of f(x)=5(x–8)²–1 into the graph of g(x)=5(x–5)²+5 is a translation 3 units to the right and 6 units up.

Here's the step-by-step explanation:

1. The general form of a quadratic function is f(x) = a(x - h)² + k, where (h, k) is the vertex of the parabola.

2. For f(x), the vertex is (8, -1). For g(x), the vertex is (5, 5).

3. To go from (8, -1) to (5, 5), you would move 3 units to the right (8 - 3 = 5) and 6 units up (-1 + 6 = 5).

So, the correct answer is "translation 3 units right and 6 units up".

Question

The transformation that converts the graph of f(x)=5(x–8)²–1 into the graph of g(x)=5(x–5)²+5 is a translation 3 units to the right and 6 units up.

Here's the step-by-step explanation:

1. The general form of a quadratic function is f(x) = a(x - h)² + k, where (h, k) is the vertex of the parabola.

2. For f(x), the vertex is (8, -1). For g(x), the vertex is (5, 5).

3. To go from (8, -1) to (5, 5), you would move 3 units to the right (8 - 3 = 5) and 6 units up (-1 + 6 = 5).

So, the correct answer is "translation 3 units right and 6 units up".

Knowee AI · Accepted Answer

The transformation that converts the graph of f(x)=5(x–8)²–1 into the graph of g(x)=5(x–5)²+5 is a translation 3 units to the right and 6 units up.

Here's the step-by-step explanation:

1. The general form of a quadratic function is f(x) = a(x - h)² + k, where (h, k) is the vertex of the parabola.

2. For f(x), the vertex is (8, -1). For g(x), the vertex is (5, 5).

3. To go from (8, -1) to (5, 5), you would move 3 units to the right (8 - 3 = 5) and 6 units up (-1 + 6 = 5).

So, the correct answer is "translation 3 units right and 6 units up".

What kind of transformation converts the graph of f(x)=5(x–8)2–1 into the graph of g(x)=5(x–5)2+5?translation 6 units left and 3 units uptranslation 3 units left and 6 units uptranslation 3 units right and 6 units downtranslation 6 units right and 3 units downSubmit