1

ROSE

Rose Vocabulary

Definition / Example
Cubic Equation
Polynomial Equation
Principal Square Root
Quadratic Equation
Radical Sign
Solution Set
Square Root
Standard Form of a Quadratic Equation
Sum
Trinomial Square

Lesson 30

Solving Quadratics by Graphing Notes

Example OneExample Two

Solve the equation x2 = 9. Solve the equation x2 – 9 = 0.

Example ThreeExample Four

Is 0 a solution to 5x2 - x = 0?Is 0 a solution to

x4 + 3x3 - 2x2 + 1 = 0?

Example FiveExample 6

Is 5 a solution to So, how many solutions

x4 + 3x3 - 2x2 + 1 = 0?does .5x4 - 4x2 + 5 = 0

have?

Try solving these by graphing:

1. x2 + 2x - 15 = -122. x2 = 2x

Lesson 30

Solving Quadratics by Graphing Notes

3. |x + 1| = 04. |x| = 25

5. x2 = 256. x3 + 4x2 - 5x = 0

Lesson 30

Solving Quadratics by Graphing

DOK 1

Use your graphing calculator to solve these equations. Graph the equations below and write your solution sets. Make sure zero is on the right!!

1. x2 + 2x – 15 = -122. x2 + 2x – 15 = -7

3. x2 = 2x4. |x| = 5

5. |x + 1| = 0 6. x2 = 25

Lesson 30

Solving Quadratics by Graphing

DOK 2

7. Solve for x using your calculator: x3 + 4x2 – 5x = 0

8. How many solutions does the equation x5–3x4–x3+4x2–12x+1=0

have? How do you know?

9. A football is kicked into the air. The formula h = 25t – 5t2
approximates the height (h) in meters of the football above the
ground after t seconds.

a) Graph the equation y = 25x – 5x2 and fill in the table.

X / Y1

b) What is the height of the football after 2 seconds?

c) When will the football be 20 meters above the ground?

d) When will the ball hit the ground?

Lesson 31

Solving Quadratics by Factoring Notes

Important To Know!

To solve a quadratic by factoring you need to:

1. Set your equation equal to zero

2. Factor completely

3. Set each factor equal to zero

4. Solve each factor for the variable

5. Write your solution set

Example OneExample Two

x2 - 4x - 21 = 02k3 - 5k2 - 3k = 0

Example ThreeExample Four

x2 = 121x2 - 3x - 10 = 0

Example FiveExample Six

x2 = 8x3x2 - 2 = x2 + 6

Lesson 31

Solving Quadratics by Factoring

DOK 1

Solve by factoring. You must show all work! (Hint: set equal to ZERO)

1. x2 – 11x + 28 = 02. y2 – 16y = 0

3. 2w2 – 3w = 54. x2 – 6x – 27 = 0

5. 16x2 + 24x + 9 = 06. 3x2 + 11x – 4 = 0

7. m3 – m = 08. k3 – k2 = 30k

DOK 2

9. Marcie solved 2x2 + 5x + 2 = 5 this way:

2x2 + 5x + 2 = 5

(2x + 1)(x + 2) = 5

2x + 1 = 5 x + 2 = 5

x = 2 or x = 3

But when she checked her answers in the original equation, neither answer was a solution. What was wrong with her procedure?

Lesson 32

The Quadratic Formula Notes

Important To Know!

MUST FIRST SET THE QUADRATIC EQUATION EQUAL TO ZERO. THIS FORMULA ONLY WORKS ON QUADRATICS (DEGREE OF 2!)

QUADRATIC FORMULA

Example OneExample Two

x2 + 10x + 21 = 0x2 + 8 = 6x

Example Three

12x2 = 13x - 3

Lesson 32

The Quadratic Formula

DOK 1

1. Fill in the chart below:

Standard Form / Degree / Name
ax + b = 0 / 1
ax2 + bx + c = 0 / 2
ax3 + bx2 + cx + d = 0 / 3
ax4 + bx3 + cx2 + dx + e = 0 / 4

Any quadratic equation can be written in the form ax2+bx+c=0 where a≠0. Solving this equation by completing the square gives the formula for finding the solutions of any quadratic equation:

DOK 2

Solve the following quadratic equations using the quadratic equation.

(Hint: set equal to zero)

2. x2 – 15x + 54 = 03. 2x2 – 5x = 7

4. 2x2 – 10x = 05. 3x2 – 10x – 8 = 0

6. x2 – 10x + 25 = 07. 24 – 22x + 4x2 = 0

Lesson 33

Completing the Square

DOK 1

Find the value of c that makes each trinomial a perfect square.

1. x2 – 16x + c2. y2 – 10y + c

3. p2 – 7p + c4. c + 11m + m2

DOK 2

Solve each equation by completing the square.

5. x2 – 4x – 12 = 0

6. c2 + 20c + 11 = 200

7. x2 + 4x + 3 = 0

8. d2 + 3d – 10 = 0

Algebra One: Unit Nine ~ Solving Quadratic Equations desotocountyschools.org/shs Maggie Dennis & Karen Hatch