U8L1-L4 Review

Solving Quadratics Review (All Methods)

Unit 8, Lessons 1-4

Solving Quadratics by Factoring

ALWAYS check for a GCF first and factor it out if it exists.

​Don't Forget!

• When a trinomial is present or can be created

• The difference of two squares

When to Attempt Use:

Multiple Choice

What is the first step to solving a quadratic equation by factoring?

• Factor into two binomials

• Make a t-chart

• Check for a greatest common factor (GCF)

• Slide and divide

Multiple Choice

What is the factored form of x² - 5x - 6?

• (x - 3)(x - 2)

• (x - 6)(x + 1)

• (x - 6)(x - 1)

• (x - 3)(x + 2)

Dropdown

When solving the equation 2n² + 3n - 9, you should first​

Select answer

. Afterwards, you should​

Select answer

. Multiply so that the new trinomial now says n² + 3n - 18. Next, make a list of the factors of​ -18 . The two factors that multiply to make -18 and sum to make 3 are ​

Select answer

. So the new trinomial is ​

Select answer

. However, we must divide by the number we slid, so the correct factorization is ​

Select answer

.

Solve Using Square Roots

• It might look like there is a "b" term present, but always check to see if that term is being squared.

• You CANNOT square root until the sauare is ISOLATED!

• When you square root a number, you must write ±

Don't Forget!

• When there is no "b" term present.

• When you can easily take the square root of both sides of an equation.

When to Use:

Labeling

Label the equation with a "Yes" if you can solve it using square roots and a "No" if you cannot.

Drag labels to their correct position on the image

Yes

No

Labeling

Label the equation with a "Yes" if you can solve it using square roots and a "No" if you cannot.

Drag labels to their correct position on the image

No

Yes

Labeling

Label the equation with a "Yes" if you can solve it using square roots and a "No" if you cannot.

Drag labels to their correct position on the image

Yes

No

Labeling

Label the equation with a "Yes" if you can solve it using square roots and a "No" if you cannot.

Drag labels to their correct position on the image

No

Yes

Labeling

Label the equation with a "Yes" if you can solve it using square roots and a "No" if you cannot.

Drag labels to their correct position on the image

Yes

No

Labeling

Label the equation with a "Yes" if you can solve it using square roots and a "No" if you cannot.

Drag labels to their correct position on the image

Yes

No

Multiple Choice

• {49,-49}

• {8,-8}

• {7,-7}

• No Solution

Multiple Choice

• {10,-10}

• No Solution

• {10.12,-10.12}

• {100}

Multiple Choice

Solve:  $$7x^2=-21$$  

• $$x=\pm\sqrt{3}$$  

• No real solution

• $$x=\pm2\sqrt{7}$$  

• $$x=\pm\sqrt{14}$$  

Multiple Choice

(x + 1) ² = 25

• ± 5
• 4  or  -6
• -4  or  6
• ± 4

Solve by Completing the Square

• You have to isolate the constant FIRST!

• Cut b in half, square the result, and add that to BOTH sides.

​Don't Forget!

• When a = 1 and b is even

When to Use

Reorder

Reorder the following steps for solving a quadratic equation by completing the square.

• Isolate the constant term

• Cut b in half and square the result.

• Add the final result to both sides.

• Rewrite the completed square trinomial in factored form.

• Solve the equation for x.

1

2

3

4

5

• 1
• 2
• 3
• 4
• 5

Multiple Choice

What do you need to add in order to complete the square?

x² + 6x = 20

• 9
• 100
• 36
• 12

Multiple Choice

What are the solutions to the following equation?

x² + 6x = 20

• -3 ± √23

• -3 ± √29

• -6 ± √23

• -6 ± √20

Multiple Choice

Solve by completing the square.

x² + 8x + 3 = 17

• 4 ± √30

• - 4 ± √30

• 2 or -10

• -2 or 10

Solve Using The Quadratic Formula

• It's easier to find the discriminant first (b² - 4ac) and then plug into the formula once that is simplified.

​Don't Forget!

• When no other method will work

• If you just really like the formula

When to Use:

Multiple Choice

Which expression below represents the discriminant?

• ax² + bx + c

• b - 4ac

• b² - 4ac

• b² + 4ac

Multiple Choice

If the discriminant equals 0, then the quadratic has:

• 1 Repeated Solution

• 2 Distinct and Real Solutions

• No solution

• 2 Imaginary Solutions

Multiple Choice

Determine the values of
a, b, and c for
the quadratic equation: 
4x² – 8x = 3

• a = 4, b = -8, c = 3
• a = 4, b =-8, c =-3
• a = 4, b = 8, c = 3
• a = 4, b = 8, c = -3

Multiple Choice

What is missing from the Quadratic Formula?

• 2

• 4

• c

• b

Multiple Choice

What's missing from the Quadratic formula?

• -a

• -b

• 2a

• x

Multiple Choice

What is missing from the Quadratic Formula?

• WHY ARE THERE SO MANY LETTERS?!

• c

• - b

• x

Multiple Choice

What is missing from the Quadratic Formula?

• b

• a

• d

• 4a

Multiple Choice

What is missing from the Quadratic Formula?

• b

• 2

• b²

• x

Multiple Choice

What does the discriminant determine?

• Whether the graph goes up or down

• The vertex

• The number of Solutions

• The y-intercept

Multiple Choice

If the discriminant is positive, how many solutions does the graph have?

• 2

• 1

• 0

Multiple Choice

If the discriminant is negative, how many solutions does the graph have?

• 2

• 1

• 0

Multiple Choice

If the discriminant is zero, how many solutions does the graph have?

• 2

• 1

• 0

Multiple Choice

A function has a discriminant of 25.
How many solutions does it have?

• 0
• 1
• 2
• 5

Multiple Choice

A function has a discriminant of -3.
How many x-intercepts (solutions) does it have?

• 0
• 1
• 2
• 3

Multiple Choice

What is the discriminant of -2x² − x − 1 = 0

• 76

• -7

• 9

• none of these

Multiple Choice

Solve using the quadratic formula.
2x² - 9x - 35 = 0

• x = 7/2, x = -6
• x = -5/2, x =5
• x = -3/7, x =6
• x = -5/2, x = 7

Multiple Choice

Solve using the quadratic formula.

9x² = 4 + 7x

• No solution

Choose Your Method!!!

Solve the following equations on the next slides using the method of your choice. If a method doesn't work, try a different one.

​

Now you get to choose!

Multiple Choice

What are the zeros?

• x= 0 and x= -4
• x= 0 and x= 4
• x = -1 and x = 5

• x= -4 and x = 4

Multiple Choice

Solve.

2x² - 3x - 2 = 0

• x = 1, x = -1

• x = -1/2, x = 2

• x = 1/2, x = 2

• x = 1/2, x = 1

Multiple Choice

Solve.

$$4\left(x-5\right)^2=12$$  

• (4x + 20)² = 12

• x = 5 ± √3

• x = -5 ± √3

• x = 5 ± (1/2)√3

Multiple Choice

Solve

x² = 7x + 18

• -7 and -18

• 9 and 2

• 9 and -2

• 2 and 7

Multiple Choice

Solve.

-5x² = -50

• ± 5

• ± 10

• ± √10

• -10

Multiple Choice

Solve for x: 
(x+6)²=49

• x=7,12
• x=±7
• x=1,-13
• x=43,-55

Multiple Choice

What are the solutions to the following equation?

Multiple Choice

Solve.

7x² = -21

• √3
• ±√3
• -3
• No real solution