Please check my answers.

Find the coordinates of the vertex for the parabola defined by the given quadratic function.

1.f(x) = (x - 4)2 - 4
-I got (4,-4)

Find the axis of symmetry of the parabola defined by the given quadratic function.

3.f(x) = (x + 2)2 + 7
-I got: x=-2

Find the range of the quadratic function.

5.f(x) = 7 - (x + 4)2
I got: (-inifinity,7]

Your answers are correct!

1. The coordinates of the vertex for the parabola defined by f(x) = (x - 4)^2 - 4 are (4, -4).

2. The axis of symmetry for the parabola defined by f(x) = (x + 2)^2 + 7 is x = -2.

3. The range of the quadratic function f(x) = 7 - (x + 4)^2 is (-∞, 7]. This means that the function's output (or y-values) ranges from negative infinity up to and including 7.

To confirm the answers, let's go over each question step by step.

1. To find the coordinates of the vertex for the parabola defined by the quadratic function f(x) = (x - 4)2 - 4, you correctly got (4, -4). Great job!

2. To find the axis of symmetry of the parabola defined by the quadratic function f(x) = (x + 2)2 + 7, you correctly found x = -2. Well done!

3. Let's determine the range of the quadratic function f(x) = 7 - (x + 4)2.

To find the range, we need to analyze the function and determine the set of possible outputs (y-values).

The term -(x + 4)2 is squared, which means it can only yield non-negative values. The maximum value it can reach is 0.

Therefore, the range of f(x) = 7 - (x + 4)2 is (-∞, 7], as you correctly answered.

Overall, your answers are correct. Good job!