Topic 1: Graphing Quadratic Function
Definitions:
Parabola - the graph of any quadratic function
Axis of Symmetry - a vertical line that divides the parabola into two congruent halves
Vertex - the point at which the axis of symmetry intersects the parabola (the maximum or minimum)
Helpful Hints:
Video Examples:
Introduction to Quadratic Functions
Parabola - the graph of any quadratic function
Axis of Symmetry - a vertical line that divides the parabola into two congruent halves
Vertex - the point at which the axis of symmetry intersects the parabola (the maximum or minimum)
Helpful Hints:
- a is the coefficient of the squared term, b is the coefficient of the linear term, and c is the constant
- axis of symmetry: x = -b/2a
- vertex happens at the highest or lowest point, to get it the y value of the coordinate take the x value of the axis of symmetry and plug it back into your origional function (the y value is also the maximum or minimum value)
- the parabola has a maximum if the a value is negative, the parabola has a minimum if the a value is positive
- the y-intercept is always the c value
Video Examples:
Introduction to Quadratic Functions
How to Find the Vertex and Axis of Symmetry
Graphing Quadratic Inequalities
Topic 2: Solving Quadratic Equations by Graphing
Definitions:
Roots- solutions or x-intercepts of a quadratic function
Zeros - solutions or x-intercepts of a quadratic function
Helpful Hints:
Video Examples:
Determining Solutions by Graphing
Roots- solutions or x-intercepts of a quadratic function
Zeros - solutions or x-intercepts of a quadratic function
Helpful Hints:
Video Examples:
Determining Solutions by Graphing
Writing the Factored form of a Function from Zeros
Solving Quadratics by Factoring
Topic 3: Factoring Sums of Squares
Helpful Hints:
Factoring Sums of Squares
- you must use conjugates
Factoring Sums of Squares
Topic 4: Discriminant and the Quadratic Formula
Definitions:
discriminant: b^2 -4ac (the part inside the square root)
Helpful Hints:
Video Examples:
Using the Discriminant to Determine the Number of Solutions
discriminant: b^2 -4ac (the part inside the square root)
Helpful Hints:
Video Examples:
Using the Discriminant to Determine the Number of Solutions
Using the Quadratic Formula to Solve
Fundamental Thm. of Algebra
Topic 5: Analyzing Quadratic Functions
Definitions:
vertex form- y = a(x-h)^2 + k where h moves left and right (opposite of what you think) and k moves up and down (goes with what you think)
Helpful Hints:
Video Examples:
Writing the Equation of a Parabola given a Graph
vertex form- y = a(x-h)^2 + k where h moves left and right (opposite of what you think) and k moves up and down (goes with what you think)
Helpful Hints:
- vertex is at (h, k)
- axis of symmetry goes through x = h
- if the a value is positive the parabola opens up (makes a smiley face), if the a value is negative the parabola opens down (makes a frowny face)
Video Examples:
Writing the Equation of a Parabola given a Graph
Stating Translations from Vertex Form
Topic 6: Operations on Complex Numbers
Definitions:
complex number - a number that can be expressed in the form of a + bi, where a and b are real numbers and i is imaginary, (a is the real part an b is the imaginary part)
Helpful Hints:
Video Examples:
Operations on Complex Numbers
complex number - a number that can be expressed in the form of a + bi, where a and b are real numbers and i is imaginary, (a is the real part an b is the imaginary part)
Helpful Hints:
- you can only add real with real and imaginary with imaginary
Video Examples:
Operations on Complex Numbers