Algebra Tutorials!
Saturday 15th of June
Calculations with Negative Numbers
Solving Linear Equations
Systems of Linear Equations
Solving Linear Equations Graphically
Algebra Expressions
Evaluating Expressions and Solving Equations
Fraction rules
Factoring Quadratic Trinomials
Multiplying and Dividing Fractions
Dividing Decimals by Whole Numbers
Adding and Subtracting Radicals
Subtracting Fractions
Factoring Polynomials by Grouping
Slopes of Perpendicular Lines
Linear Equations
Roots - Radicals 1
Graph of a Line
Sum of the Roots of a Quadratic
Writing Linear Equations Using Slope and Point
Factoring Trinomials with Leading Coefficient 1
Writing Linear Equations Using Slope and Point
Simplifying Expressions with Negative Exponents
Solving Equations 3
Solving Quadratic Equations
Parent and Family Graphs
Collecting Like Terms
nth Roots
Power of a Quotient Property of Exponents
Adding and Subtracting Fractions
Solving Linear Systems of Equations by Elimination
The Quadratic Formula
Fractions and Mixed Numbers
Solving Rational Equations
Multiplying Special Binomials
Rounding Numbers
Factoring by Grouping
Polar Form of a Complex Number
Solving Quadratic Equations
Simplifying Complex Fractions
Common Logs
Operations on Signed Numbers
Multiplying Fractions in General
Dividing Polynomials
Higher Degrees and Variable Exponents
Solving Quadratic Inequalities with a Sign Graph
Writing a Rational Expression in Lowest Terms
Solving Quadratic Inequalities with a Sign Graph
Solving Linear Equations
The Square of a Binomial
Properties of Negative Exponents
Inverse Functions
Rotating an Ellipse
Multiplying Numbers
Linear Equations
Solving Equations with One Log Term
Combining Operations
The Ellipse
Straight Lines
Graphing Inequalities in Two Variables
Solving Trigonometric Equations
Adding and Subtracting Fractions
Simple Trinomials as Products of Binomials
Ratios and Proportions
Solving Equations
Multiplying and Dividing Fractions 2
Rational Numbers
Difference of Two Squares
Factoring Polynomials by Grouping
Solving Equations That Contain Rational Expressions
Solving Quadratic Equations
Dividing and Subtracting Rational Expressions
Square Roots and Real Numbers
Order of Operations
Solving Nonlinear Equations by Substitution
The Distance and Midpoint Formulas
Linear Equations
Graphing Using x- and y- Intercepts
Properties of Exponents
Solving Quadratic Equations
Solving One-Step Equations Using Algebra
Relatively Prime Numbers
Solving a Quadratic Inequality with Two Solutions
Operations on Radicals
Factoring a Difference of Two Squares
Straight Lines
Solving Quadratic Equations by Factoring
Graphing Logarithmic Functions
Simplifying Expressions Involving Variables
Adding Integers
Factoring Completely General Quadratic Trinomials
Using Patterns to Multiply Two Binomials
Adding and Subtracting Rational Expressions With Unlike Denominators
Rational Exponents
Horizontal and Vertical Lines
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The graph of a quadratic expression has a U-shaped graph called a parabola. We can write a quadratic expression in the form ax2 + c, where a is called the leading coefficient. The way the parabola opens depends on the sign of the leading coefficient. In fact, if a is positive, the parabola opens up; if a is negative, the parabola opens down. If the absolute value of a is greater than 1, then the parabola is narrower than y = x2. If the absolute value of a is less than 1, then the parabola is wider than y = x2

A quadratic function can be written in different forms. Each form gives information about the graph.

Standard Form (no linear term)


y = -3x2 + 4 matches .

“This quadratic function is written in standard form. Because the leading coefficient is negative, the graph opens down. The 3 causes the graph to be narrower than y = x2. The vertex is at (0, 4), because the graph has been shifted upward 4 units. You can test the ordered pair (1, 1). When x = 1, y = -3(1)2 + 4, which is 1.”

y = ax2 + c Graphical Information

c > 0: vertical shift upward of c units

c < 0: vertical shift downward of c units


y = (x + 3)2 + 1 matches .

“This quadratic function can be written in vertex form as The vertex is at The graph opens up because a is positive.”

Vertex Form
  y = a(x - h)2 + k Graphical Information

 vertex at (h, k)


matches . “This quadratic function is written in factored form. The graph opens down because a is less than 0. Because the graph is wider than y = x2. The intercepts are at (-5, 0) and (2, 0)”

Factored Form
y = a(x - p)(x - q) Graphical Information

x-intercepts at (p, 0) and (q, 0)

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