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we have

Let

y=f(x)

Step

Find the equation in vertex form

Group terms that contain the same variable, and move the constant to the opposite side of the equation

Complete the square. Remember to balance the equation by adding the same constants to each side

Rewrite as perfect squares

therefore

the equation in vertex form is equal to

Step

Find the vertex of the function

the vertex of the function is the point

Step

Find the axis of symmetry

we know that

the function is a vertical parabola. therefore the axis of symmetry is the coordinate x of the vertex

the vertex of the function is the point

so

the axis of symmetry is

Step

Find the y-intercept of the function

we know that

the y-intercept is the value of the function when the value of x is equal to zero

so

for

the y-intercept of the function is equal to the point

Step

using a graph tool

see the attached figure

The function crosses the x-axis twice

Statements

1) The function in vertex form is f(x) = (x – 4)2 – 11> is true

2) The vertex of the function is (–8, 5) > is false

3) The axis of symmetry is x = 5 > is false

4) The y-intercept of the function is (0, 5) > is true

5) The function crosses the x-axis twice > is true