The transformation that converts the graph of f(x) = -8(x+4)^2 + 1 into the graph of g(x) = -8(x+9)^2 + 8 is a horizontal shift to the left by 5 units and a vertical shift upwards by 7 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 f(x), the vertex is at (-4, 1). For g(x), the vertex is at (-9, 8).

3. Comparing the vertices of the two functions, we see that the x-coordinate has decreased by 5 (from -4 to -9), which corresponds to a shift to the left by 5 units.

4. Similarly, the y-coordinate has increased by 7 (from 1 to 8), which corresponds to a shift upwards by 7 units.

So, the transformation is a horizontal shift to the left by 5 units and a vertical shift upwards by 7 units.

Question

The transformation that converts the graph of f(x) = -8(x+4)^2 + 1 into the graph of g(x) = -8(x+9)^2 + 8 is a horizontal shift to the left by 5 units and a vertical shift upwards by 7 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 f(x), the vertex is at (-4, 1). For g(x), the vertex is at (-9, 8).

3. Comparing the vertices of the two functions, we see that the x-coordinate has decreased by 5 (from -4 to -9), which corresponds to a shift to the left by 5 units.

4. Similarly, the y-coordinate has increased by 7 (from 1 to 8), which corresponds to a shift upwards by 7 units.

So, the transformation is a horizontal shift to the left by 5 units and a vertical shift upwards by 7 units.

Knowee AI · Accepted Answer

The transformation that converts the graph of f(x) = -8(x+4)^2 + 1 into the graph of g(x) = -8(x+9)^2 + 8 is a horizontal shift to the left by 5 units and a vertical shift upwards by 7 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 f(x), the vertex is at (-4, 1). For g(x), the vertex is at (-9, 8).

3. Comparing the vertices of the two functions, we see that the x-coordinate has decreased by 5 (from -4 to -9), which corresponds to a shift to the left by 5 units.

4. Similarly, the y-coordinate has increased by 7 (from 1 to 8), which corresponds to a shift upwards by 7 units.

So, the transformation is a horizontal shift to the left by 5 units and a vertical shift upwards by 7 units.

What kind of transformation converts the graph of f(x)=–8(x+4)2+1 into the graph of g(x)=–8(x+9)2+8?

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