The quadratic function that satisfies all these conditions is f(x) = -2(x - 6)² + 4.

Here's why:

1. The maximum value of the function is 4, which occurs at x = 6. This tells us that the vertex of the parabola is at (6, 4).

2. The axis of symmetry of a parabola is the vertical line that passes through the vertex. Since the vertex is at (6, 4), the axis of symmetry is x = 6.

3. The x-intercept of the function is the value of x for which f(x) = 0. If we set -2(x - 6)² + 4 = 0 and solve for x, we get x = 8, which is the given x-intercept.

4. The y-intercept of the function is the value of f(x) when x = 0. If we substitute x = 0 into the function, we get -2(0 - 6)² + 4 = -32, which is the given y-intercept.

Therefore, the function that satisfies all these conditions is f(x) = -2(x - 6)² + 4.

Question

The quadratic function that satisfies all these conditions is f(x) = -2(x - 6)² + 4.

Here's why:

1. The maximum value of the function is 4, which occurs at x = 6. This tells us that the vertex of the parabola is at (6, 4).

2. The axis of symmetry of a parabola is the vertical line that passes through the vertex. Since the vertex is at (6, 4), the axis of symmetry is x = 6.

3. The x-intercept of the function is the value of x for which f(x) = 0. If we set -2(x - 6)² + 4 = 0 and solve for x, we get x = 8, which is the given x-intercept.

4. The y-intercept of the function is the value of f(x) when x = 0. If we substitute x = 0 into the function, we get -2(0 - 6)² + 4 = -32, which is the given y-intercept.

Therefore, the function that satisfies all these conditions is f(x) = -2(x - 6)² + 4.

Knowee AI · Accepted Answer

The quadratic function that satisfies all these conditions is f(x) = -2(x - 6)² + 4.

Here's why:

1. The maximum value of the function is 4, which occurs at x = 6. This tells us that the vertex of the parabola is at (6, 4).

2. The axis of symmetry of a parabola is the vertical line that passes through the vertex. Since the vertex is at (6, 4), the axis of symmetry is x = 6.

3. The x-intercept of the function is the value of x for which f(x) = 0. If we set -2(x - 6)² + 4 = 0 and solve for x, we get x = 8, which is the given x-intercept.

4. The y-intercept of the function is the value of f(x) when x = 0. If we substitute x = 0 into the function, we get -2(0 - 6)² + 4 = -32, which is the given y-intercept.

Therefore, the function that satisfies all these conditions is f(x) = -2(x - 6)² + 4.

Select the correct answer.Select the quadratic function with a graph that has the following features.x-intercept at (8,0)y-intercept at (0,-32)maximum value at (6,4)axis of symmetry at x = 6

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