The transformation that converts the graph of f(x)=2(x–3)²+7 into the graph of g(x)=2(x–8)²+10 is a horizontal shift to the right by 5 units and a vertical shift up by 3 units.

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 the function f(x)=2(x–3)²+7, the vertex is at (3,7).

3. For the function g(x)=2(x–8)²+10, the vertex is at (8,10).

4. To go from (3,7) to (8,10), you move 5 units to the right (which is a horizontal shift) and 3 units up (which is a vertical shift).

So, the transformation is a horizontal shift to the right by 5 units and a vertical shift up by 3 units.

Question

The transformation that converts the graph of f(x)=2(x–3)²+7 into the graph of g(x)=2(x–8)²+10 is a horizontal shift to the right by 5 units and a vertical shift up by 3 units.

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 the function f(x)=2(x–3)²+7, the vertex is at (3,7).

3. For the function g(x)=2(x–8)²+10, the vertex is at (8,10).

4. To go from (3,7) to (8,10), you move 5 units to the right (which is a horizontal shift) and 3 units up (which is a vertical shift).

So, the transformation is a horizontal shift to the right by 5 units and a vertical shift up by 3 units.

Knowee AI · Accepted Answer

The transformation that converts the graph of f(x)=2(x–3)²+7 into the graph of g(x)=2(x–8)²+10 is a horizontal shift to the right by 5 units and a vertical shift up by 3 units.

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 the function f(x)=2(x–3)²+7, the vertex is at (3,7).

3. For the function g(x)=2(x–8)²+10, the vertex is at (8,10).

4. To go from (3,7) to (8,10), you move 5 units to the right (which is a horizontal shift) and 3 units up (which is a vertical shift).

So, the transformation is a horizontal shift to the right by 5 units and a vertical shift up by 3 units.

What kind of transformation converts the graph of f(x)=2(x–3)2+7 into the graph of g(x)=2(x–8)2+10?

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