Question

Can you please help me with the following problems?

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

1.f(x) = (x - 4)2 - 4

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

3.f(x) = (x + 2)2 + 7

Find the range of the quadratic function.

5.f(x) = 7 - (x + 4)2

Answer 1

for any parabola of the form
f(x) = a(x-h)^2 + k
the vertex is (h,k) and the axis of symmetry is x = h

Make use of that fact for #1 and #3

The range is the set of y values that the graph covers.
so in #5 first rewrite it as
f(x) = -(x+4)^2 - 7

Wouldn't the vertex be (-4,-7) and since the parabola opens downwards, what do you thing would be the y values covered by the graph?

Answer 2

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]

Answer 3

find the coordinates of the vertex for the parabola defined by the given quadratic function f(x)=(x+7)^2-6