Methods to Solving the Quadratic

Equation Foldable

Created by Ms.Nhotsoubanh

Relax about the quadratic equation. There are so many ways to solve it.

Materials you will need…

• Construction Paper (soft colors) or computer paper

• Scissors• Markers (2 to 3 Dark colors)• Pen or Pencil• ruler

Directions:• Lay your construction horizontally so that we are

folding the 17 inches in half.– We want the largest viewing area as possible.

• Fold your construction paper in half, vertically down the middle (taco style).

• Fold both ends of the construction paper inward so that they meet at the center crease.

• Using a ruler, measure approximately one and a half inches from the top and mark it.

• Do the same for the other side.• Cut off the piece from both sides. Do not cut too much.

– This will be front of your foldable; your heading will be displayed here.

Heading

• Using one of your markers, write “Methods to Solving Quadratic Equations” in the top as your heading.

• Measure about 5 inches from the top and mark both sides of the front cover.

• Using your scissors, cut to the first crease. DO NOT CUT ALL THE WAY. (cut along the red lines)– The foldable should start taking form.

Methods to solving Quadratic Equations

scrapscrap

Sections

• Close the flaps so that you can see the front of your cover; you should see 4 individual parts.

• Using a marker, label each part as follows:» Factoring by Grouping» Factoring by x-Box» Quadratic Formula» Square Root Principle

Methods to Solving Quadratic Equations

Square Root

Principle

Quadratic Formula

Factoring by x-Box

Factoring by Grouping

THIS IS HOW YOUR FOLDABLE WILL LOOK WHEN IT IS

COMPLETED

Methods to solving Quadratic Equations

By Grouping:

By the Quadratic Formula:

Example 3

By x-Box:

By Square Root Principle:

Example 4

Your turn

Your turn

Your turn

Your turn

Example 1 Example 2

By Grouping:

Example 1: Solve: 5x2 + 7x – 6 = 0

Your turn: Solve: 3x2 – 12x – 15 = 0

-30

7b

a(c)

-3 10

a(c)

b

Factors of a(c) that will give you b

1st term last term

5x2 – 6 = 0 + 10x – 3x ( ) ( )

x(5x – 3) + 2(5x – 3) = 0 Factor out gcf for each binomial

(x + 2) (5x – 3) = 0

x + 2 = 0 5x – 3 = 0x = -2 +3 +3

5x = 3 5 5 x =

x = { -2, }

Solve for x

Standard form for a quadratic equation is ax2 + bx + c = 0

By x-Box

Example 2: Solve: 5x2 + 7x – 6 = 0

-30

7b

a(c)

-3 10

Last term

1st Term

Factor

Factor

5x2

-6

+10x

-3x

Place the factors: 10 & -3 in the

box and add an x to each

x

5x

+2

-3Then factor out gcf for

each binomial

(x + 2) (5x – 3) = 0

x + 2 = 0 5x – 3 = 0x = -2 +3 +3

5x = 3 5 5 x =

x = { -2, }

Your turn: Solve: 3x2 – 12x – 15 = 0

Solve for x

Standard form for a quadratic equation is ax2 + bx + c = 0

By the Quadratic Formula

Example 3: Solve: 5x2 + 7x – 6 = 0

1. Define a, b, and c.

2. Write the quadratic formula.

3. Substitute the given values into the formula.

Steps:

a = _____b = _____c = ___

57

4. Solve for x. (you should have 2 answers)

-6

Your turn: Solve: 3x2 – 12x – 15 = 0

Standard form for a quadratic equation is ax2 + bx + c = 0

x = { -2, }

By the Square Root Principle

Example 4: Solve: 2x2 – 32 = 0

Standard form for a quadratic equation is ax2 + bx + c = 0

Here is the exception, when there is no “b”, you get: ax2 + c = 0

1.Isolate the x2 term.

2. Take the square root of both sides (that gets rid of the “square”, just like when solving radical equations)

3. Solve for x. (you should have 2 answers)

Steps:

2x2 – 32 = 0 +32 +322x2 = 32 2 2 x2 = 16

Your turn: 3x2 – 27 = 0