# Graphing Functions: Completing the Square, Quadratic Functions, Axis of Symmetry, and Intercepts

1. Using completing the square to describe the graph of the following function. Support your answer graphically.

f(x) = -2x^2 + 4x + 1

2. Graph the function: g(x) = (x-2)^3

3. Determine the quadratic function f whose vertex is (3, -2) and passes through (2, 1)

4. Graph the line containing the point P and having slope m: P = (2, -7); m = 0

5. Graph the function and state the vertex, the axis of symmetry, the intercepts, if any: f(x) = x^2-6x+5

What is the vertex?

What is the axis of symmetry?

What are the intercepts, if any?

https://brainmass.com/math/graphs-and-functions/completing-square-quadratic-functions-axis-symmetry-543240

#### Solution Preview

1.

This parabola has a vertex at

We see that as the function approaches , so the vertex point is a maxima (the parabola opens down).

The parabola intersects the x-axis when

Which gives:

It intersects the y-axis when x=0 and this gives:

To summarize:

The parabola has a vertex which is a maxima at so its symmetry axis is x=1

It intersects the x-axis at and

It intersects the y-axis at ...

#### Solution Summary

The solution assists with completing the square, quadratic functions, axis of symmetry and intercepts. The axis of symmetry and intercepts are analyzed.

Cumulative Equation Problems

Ch. 10 Cumulative Problems

1) solve (X - 4)2 = 3

2) solve 5 (X - 2)2 = 3

3) solve - 9 (X - 3)2 = - 7

4) solve by completing the square 2 X2 - 8 X - 9 = 0

5) solve by completing the square 4 X2 + 2 X - 3 = 0

6) solve by using the quadratic formula 4 X2 - 3 X + 3 = 0

7) solve by using the quadratic formula 5 X2 - 7 X = 1

8) solve by using the quadratic formula 3 X2 = 11 X + 4

9) solve X2 + 12 X + 32 = 0

10) solve X2 + 5 X - 9 = 0

11) Graph the quadratic equation after completing the given table of values. Y = X2 - 1

X Y

- 2

- 1

0

1

2

12) Graph the quadratic equation after completing the given table of values. Y = - X2 + 1

X Y

- 2

- 1

0

1

2

13) Find the axis of symmetry. Y = X2 + X + 1

14) Find the axis of symmetry. Y = - X2 + 4 X + 2

15) Find the intercepts. Y = X2 - 5 X - 10

16) Find the intercepts. Y = X2 - 4 X + 4

17) The length of a rectangle is 3 cm more than 2 times its width. If the area of the rectangle is 99 cm2, find the dimensions of the rectangle to the nearest thousandth.

18) The height h in feet of an object after t seconds is given by the function

h = - 16 t 2 + 60 t + 9

How long will it take the object to hit the ground? Round your answer to the nearest thousandth.