Quadratics

Quadratics & Exponential Functions

Unit 7

Start

Index

Vocabulary

Intro

Factoring

Adding & Subtracting

Difference of Squares

Distributing & Multiplying

Dividing

Vocabulary:

Vocabulary:

Believe in your potential and always live life on your own terms!

Quadratics Module

Adding & Subtracting Polynomials

Distributing & Multiplying Polynomials

Types of Solutions

Types of Solutions

• To find a solution to a quadratic equation, set equation equal to 0

• Solutions are at x - intercept

• Also know as: x - intercepts, roots, zeroes

Two Solutions

One Solution

No Solution

Examples of Quadratics and Solutions

Solutions: x = -7 and x = -6

Sample Question 1

Parts of a Quadratic

Vertex

Maximum

Minimum

Sample Question 2

Identify the features of the quadratic:

Parts of a Quadratic

Axis of Symmetry

Quadratic Formula

• Used to find solutions to the equation:

1. Write in standard form
2. Identify a, b, and c
3. Substitute value of a, b, and c into the quadratic formula
4. Simplify
5. Split into two equations and solve for x

Quadratic Formula: DESMOS

For

Use

1. Type in DESMOS
2. Compare Decimal valuess
3. Match decimals to x-intercepts to find TWO solutions

x-intercepts:

Answer

Quadratic Formula Word Problem

1. Identify like terms
1. same base and exponent
2. SUBTRACT coefficients

Step 2

Step 1

Distribute Polynomials:

Distributing just means you take each number/variable outside the group and multiply it by every single number/variable inside the group.

The Box Method!

1. Draw the box/grid
1. rows: number of terms in first part of problem
2. columns: number of terms in second part of problem
2. Multiply outside numbers into each cell
3. If needed, combine like terms inside of cells

Multiplying Polynomials:

Multiplying polynomials is the process of taking every term in one polynomial and multiplying it by every term in the other polynomial.

The Box Method!

1. Draw the box/grid
1. rows: number of terms in first part of problem
2. columns: number of terms in second part of problem
2. Multiply outside numbers into each cell
3. If needed, combine like terms inside of cells

The FOIL Method!

First, Outer, Inner, Last

F - First: Multiply the first term in each set of parentheses.

O - Outer: Multiply the outer terms (the ones of the far ends).

I - Inner: Multiply the inner terms ( the ones in the middle).

L - Last: Multiply the last term in each set of parentheses.

Final STEP!

Factoring Polynomials Module

Factoring by GCF

Factoring

Factoring

Greatest Common Factor (GCF)

The greatest common factor, GCF, is the BIGGEST monomial that divides into each term evenly.

DESMOS hack

Factoring by the GCF

1. Find the GCF
2. Divide each coefficient by the GCF to factor each term
3. Write down factors for each term
4. GCF is on outside; everything else on the inside

Answer

DESMOS hack

Factoring by

1. Does your expression look like
2. Find factors for C
3. Write down factors for C
4. Find the factor pair that ADDs to equal B
5. Use factors to fill in answer formula:

Answer

Factoring by

1. Does your expression look like
2. Multiply A and C
3. Find factors for product of A and C
4. Find the factor pair that adds to B
1. Replace pair with B in original problem to create new pairs
5. Factor the GCF of each pair
6. Rewrite factors

Factor Pairs

Inside #'s

Outside #'s

Answer

Example 1

Factor Pairs

Answer

Polynomials Module Pt. 3

Differenceof Squares

Dividing Polynomials

Difference of Squares

1. Do you have a binomial?
2. Find the square roots of both terms
3. Write factors in this form:

Dividing Polynomials

1. Set up box
2. Put divisor (bottom number/variable) on the outside
3. Put the dividend (top numbers/variables) on the inside
4. Divide outside by each inside term
5. Write as a polynomial

Answer

Example 2

Two Solutions

• Touches the x-axis TWO times

Factor each pair!

Step 1

1. Identify Like Terms
1. Same base AND same exponent

Example 2

Answer

Example 2

Answer

Example 1

Answer

Inside #'s

Outside #'s

DESMOS: Find the GCF

Combine Like Terms

One Solution

• Touches the x-axis ONE time

Example 2

DESMOS: Find the GCF

No Solution

• Never touches x-axis

Step 2

1. Subtract coefficients

Example 1

Example 1

Answer

Minimum

• The lowest point, at the vertex

y = 1

Example 1

Inside #'s

Outside #'s

Axis of Symmetry

• Invisible vertical line that passes through the vertex.

x = -2

Factor each pair!

Maximum

• The highest point, at the vertex

y = 3

Subtracting Polynomials

Vertex

• The maximum or minimum point of a parabola

(-2, 1)