Solving Quadratic Equations Review

​Solving Quadratic Equations

​A quadratic equation can be solved by multiple methods

Some text here about the topic of discussion

​The following are all methods to solve a quadratic equation:

• ​ Graphing

• Factoring

• Square Root Property

• Completing the Square

• Quadratic Formula​

Subject | Subject

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Multiple Choice

Which of the following is not a method to solve a quadratic equation?

• Factoring

• Finding the Vertex

• Graphing

• Quadratic Formula

​Solving by Graphing

The solution to a quadratic equation set = 0 is the x-intercepts of the equation.

This is the graph of y = x² + 2x - 5

The solutions to ​ x² + 2x - 5 = 0

are where the graph crosses the x-axis

x = -3 and x = 1​

Subject | Subject

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Multiple Choice

This is the graph of y = x² - x - 2.

What are the solutions to

x² - x - 2 = 0 ?

• x = -2

• x = -1 and x = 2

• x = 1 and x = -2

• No Solutions

​Factoring

Solve x² - 7x = -12 by factoring

​

x² - 7x + 12 = 0 Set = 0

(x - 3)(x - 4) = 0 Factor

x - 3 = 0 or x - 4 = 0​ Set each factor = 0

x = 3 or x = 4 Solve each equation for x

​

Solutions are: x = 3 or x = 4​

​

Multiple Choice

Solve the following equation by factoring

$$x^2+8x\ +\ 12\ =\ 0$$  

• x = 2 or x = 6

• x = -2 or x = -6

• x = 3 or x = 5

• x = -3 or x = -5

​Factoring out GCF

Solve 2x² - 12x = 0 by factoring

​

2x(x - 6) = 0 Factor out GCF

2x = 0 or x - 6 = 0​ Set each factor = 0

x = 0 or x = 6 Solve each equation for x

​

Solutions are: x = 0 or x = 6

​

Multiple Choice

Solve the following equation by factoring

$$x^2+8x=\ 0$$  

• x = 8

• x = 0 or x = 8

• x = -8

• x = 0 or x = -8

​Square Root Property

Multiple Choice

Solve the following equation by using the square root property

$$x^2-\ 36\ =\ 0$$  

• x = 18

• x = 0 or x = 6

• x = 6

• x = 6 or x = -6

​Complete the Square

Multiple Choice

What value of c needs to be added to make the following a perfect square

x² + 6x

• 3

• 6

• 9

• 36

Multiple Choice

Write the following as a perfect square

$$x^2-12x\ +\ 36$$  

• $$\left(x\ -\ 6\right)^2$$  

• $$\left(x-12\right)^2$$  

• $$\left(x+6\right)^2$$  

• $$\left(x+3\right)^2$$  

Multiple Choice

Solve the following equation by using the square root property

$$x^2-\ 6x\ =\ 5$$  

• $$x\ =\ 6+\sqrt[]{5}\ \ or\ x\ =\ 6-\sqrt[]{5}$$  

• $$x=\ 3+\sqrt[]{14}\$$  or $$x=3-\sqrt[]{14}$$  

• $$x=3+\sqrt[]{5}\$$  or $$x=3-\sqrt[]{5}$$  

• $$x=6+\sqrt[]{14}$$  or $$x=6-\sqrt[]{14}$$