The transformation that converts the graph of f(x)=4(x+8)²+4 into the graph of g(x)=4(x+9)²+4 is a horizontal shift to the left by 1 unit.

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. In the function f(x)=4(x+8)²+4, the vertex is at (-8, 4).

3. In the function g(x)=4(x+9)²+4, the vertex is at (-9, 4).

4. Comparing the two vertices, we can see that the x-coordinate has decreased by 1 (from -8 to -9), while the y-coordinate has remained the same.

5. Therefore, the graph of f(x) has been shifted 1 unit to the left to obtain the graph of g(x).

Question

The transformation that converts the graph of f(x)=4(x+8)²+4 into the graph of g(x)=4(x+9)²+4 is a horizontal shift to the left by 1 unit.

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. In the function f(x)=4(x+8)²+4, the vertex is at (-8, 4).

3. In the function g(x)=4(x+9)²+4, the vertex is at (-9, 4).

4. Comparing the two vertices, we can see that the x-coordinate has decreased by 1 (from -8 to -9), while the y-coordinate has remained the same.

5. Therefore, the graph of f(x) has been shifted 1 unit to the left to obtain the graph of g(x).

Knowee AI · Accepted Answer

The transformation that converts the graph of f(x)=4(x+8)²+4 into the graph of g(x)=4(x+9)²+4 is a horizontal shift to the left by 1 unit.

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. In the function f(x)=4(x+8)²+4, the vertex is at (-8, 4).

3. In the function g(x)=4(x+9)²+4, the vertex is at (-9, 4).

4. Comparing the two vertices, we can see that the x-coordinate has decreased by 1 (from -8 to -9), while the y-coordinate has remained the same.

5. Therefore, the graph of f(x) has been shifted 1 unit to the left to obtain the graph of g(x).

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