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

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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?

© BrainMass Inc. brainmass.com October 25, 2018, 8:31 am ad1c9bdddf
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.

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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.

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