Quadratic Functions Part II

0:00 Quadratic Function Forms. Standard Form, Vertex Form, and Factored Form.

2:39 Notes on the three forms.

5:37 Example: Find the Equation of a Parabola, given the Vertex and a point.

7:33 Example: Find the Equation of a Parabola, given the Two Roots and a point.

9:51 Connecting between y = 2 (x+1)(x+5) and its Graph.

12:28 Connecting between y = - 5 x^2 - x + 21 and its Graph.

17:04 Connecting between y = 2 (x - 1)(x - 5) and its Graph.

18:55 Connecting between y = - (x + 2 )^2 - 4 and its Graph.

21:42 Connecting between y = - (x + 4 )^2 - 2 and its Graph.

22:28 Connecting between y = (x - 2 )^2 and its Graph. One x- Intercept.

25:22 Given a detailed Graph, write the Function in all three forms: Vertex, Factored, and Standard.

30:34 Writing the Quadratic Equation, given a graph.

31:47 Connecting between y = x^2 +4 x + 3 and its Graph.

34:13 Connecting between y = - 3 (x + 2 )^2 + 4 and its Graph.

36:00 Connecting between y = 1/2 (x + 2 )^2 - 3 and its Graph. 37:36 Rewrite the Standard Form of f (x ) = 2 x^2 -6x + 7 in Vertex Form and identify the Max/Min Value.

40:59 Find the Domain and Range of f (x ) = - 5x^2 +9x-1.

43:09 Find the Domain and Range of f (x ) = ( x -2 )^2 +1 and g(x) = - (x+3)^2 +4. 45:15 Real-World Application.

Vertex Form.

Graphing Quadratic Functions in Standard form.

Quadratic Equations.

The Quadratic Formula.

Zero-Product Property.

Square Root Property.

Completing the Square.

The Pythagorean Theorem.

The Discriminant.

Quadratic Functions in Vertex Form.

Completing the Square.

Quadratic Functions in Standard Form.

Vertex.

Maximum or Minimum.

Axis of Symmetry.

X-Intercepts.

Y-Intercept.

Standard Form.

Factored Form.

Another Point on the Graph is knowing the axis of Symmetry and the Y-intercept.

Solve Quadratic Functions by factoring.

Graphing Quadratic Functions from Standard Form.

0:00 Quadratic Functions Part I

0:17 Vertex Form.

1:03 Factored Form.

2:27 Standard Form.

3:26 Examples.

More covered:

Features of each form.

Zeros, or Roots.

Axis of Symmetry.

The Vertex.

The Y-Intercept.

Solve by Completing the Square.

10 Examples.

Perfect Square Trinomials.

Completing the Square.

0:00 Introduction

3:59 x^2-4x-13=0

7:02 x^2-13x+36=0

9:52 x^2-x-3=0

13:01 2x^2-8x-24=0

14:56 x^2-2x+3= 0

The Quadratic Formula and the Discriminant.

Solving Quadratic Equations using the Quadratic Formula. Four Examples.