WEEK 1

DONE Unit 2: Verb Agreement

1 Topic | 3 Quizzes
DONE Unit 3: Punctuation

3 Topics | 3 Quizzes
DONE Unit 4: Apostrophes

3 Quizzes
DONE Unit 6: Using Desmos

3 Quizzes
DONE Unit 7: Ratios, Rates, and Conversions

1 Topic | 3 Quizzes
DONE Unit 8: Slope Intercept

3 Quizzes
DONE Unit 10: Line Graphs and Bar Graphs

3 Quizzes
DONE Unit 11: Scatterplots

3 Quizzes
WEEK 2

DONE Unit 12: Words in Context

3 Quizzes
DONE Unit 13: Passage Summarization

3 Quizzes
DONE Unit 14: Pronouns

3 Quizzes
DONE Unit 15: Transition Words and Phrases Part 1

1 Topic | 3 Quizzes
DONE Unit 16: Word Choice

3 Quizzes
Unit 17: Linear Word Problems – Type 1: Numbers

2 Topics | 2 Quizzes
Unit 18: Transforming Equations (Single Variable)

1 Topic | 2 Quizzes
DONE Unit 19: Systems of Linear Equations

1 Topic | 3 Quizzes
DONE Unit 20: Systems of Inequalities

1 Topic | 3 Quizzes
DONE Unit 21: Systems Word Problems

3 Quizzes
WEEK 3

DONE Unit 22: Figures and Tables

3 Quizzes
DONE Unit 23: Author’s Objective

3 Quizzes
DONE Unit 24: Misplaced Modifiers

3 Quizzes
DONE Unit 26: Statistics

1 Topic | 3 Quizzes
DONE Unit 27: Average from a Table

3 Quizzes
DONE Unit 28: Probabilities

3 Quizzes
DONE Unit 29: Percentages

1 Topic | 3 Quizzes
DONE Unit 30: Angle Problems

1 Topic | 3 Quizzes
DONE Unit 31: Circle Basics

1 Topic | 3 Quizzes
DONE Unit 32: Triangles

3 Quizzes
WEEK 4

DONE Unit 33: Accomplish the Goal

1 Topic | 3 Quizzes
DONE Unit 34: Punctuation Part 2

1 Topic | 1 Quiz
DONE Unit 35: Command of Evidence

3 Quizzes
DONE Unit 36: Parabolas and Factoring

2 Topics | 3 Quizzes
DONE Unit 37: Non-Linear Systems

1 Topic | 3 Quizzes
DONE Unit 38: Quadratic and Discriminant

3 Quizzes
DONE Unit 39: Zeros in Quadratics

3 Quizzes
DONE Unit 41: SohCahToa

3 Quizzes
WEEK 5

DONE Unit 42: Inferences

3 Quizzes
DONE Unit 43: Complete the Text

3 Quizzes
DONE Unit 44: Dual Passages

3 Quizzes
DONE Unit 45: Functions

1 Topic | 3 Quizzes
DONE Unit 46: Functions with Coordinate Box

1 Topic | 3 Quizzes
DONE Unit 47: Exponents and Radicals

1 Topic | 3 Quizzes
DONE Unit 48: Constants

1 Topic | 3 Quizzes
DONE Unit 49: Surveys and Studies

3 Quizzes
WEEK 6

DONE Unit 51: Equal Polynomials

3 Quizzes
DONE Unit 53: Area and Volume

3 Quizzes
DONE Unit 54: Absolute Value

3 Quizzes
DONE Unit 55: Box Plots

3 Quizzes
DONE Unit 56: Polynomial Graphs

3 Quizzes
DONE Unit 57: Translations

3 Quizzes
DONE Unit 58: Vertex Form of a Parabola

3 Quizzes
DONE Unit 59: Creative Geometry

3 Quizzes
EXTRA

Logical Comparisons

2 Quizzes
**Zeros in Quadratics and Other Polynomials**

One of the most crucial skills in solving quadratic problems is understanding the language used. While in real life these are slightly different terms, when referring to a single quadratic, these words all mean the same thing:

Zeros = Roots = Solutions = Real Solutions = *x*-intercepts

So when a question asks you about the zeros of a quadratic, they are asking about the *x*-intercepts.

The first graph has no intercepts, and thus no real solutions. The second is tangent to the *x*-axis, so it has one solution at *x *= 2. The third graph has solutions at *x* = 1 and *x* = 3.

**Factors**

The first graph above shows an equation that would not factor.

The second graph shows an equation where (*x* – 2) MUST be a factor, because *y* = 0 when *x *= 2.

The third graph shows an equation where (*x *-1) and (*x* – 3) MUST be factors.

If given a problem like:

An equation has roots at -1 and 5. Which if the following must be a factor?

A) \(x+5\)

B) \(x\)

C) \(x-1\)

D) \(x+1\)

**Strategy****:**

**Rebuild the factored equation by forming binomials with the given roots (solutions).**

If an equation has roots of -1 and 5, then in its factored form it would look like \((x+1)(x-5)\). This is because those binomials have solutions of -1 and 5. Thus, the answer would be D.

**Zeros in Other Equations**

The exact same concept applies if you are asked about zeros in other equations. For instance, given the graph below:

You can easily see that it has 4 x-axis intercepts, and thus would have 4 zeros or solutions.

Note that the approach above for identifying factors holds true regardless of the number of roots / solutions. If given a polynomial like:

\(ax^3+bx^2+cx+d=0\) with roots of -4, -2, and 3,

you would apply exactly the same logic.

**The halfway vertex**

If you know two zeros of a quadratic, then you actually also know the *x* value of the vertex. The vertex is always halfway between two zeros/roots/solutions/*x*-intercepts.

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