Main Concepts in Lesson:

Achievement Indicator:

AFL's Assigned to Assess

A quadratic equation is defined as an equation that has a degree of two and has only one variable.

There are two methods for solving for a quadratic equation graphically.

If a quadratic equation is in standard form graph the corresponding quadratic function and find the x-intercepts (zeroes).

If the quadratic equation is not in standard form you can graph the expression on the left side and the expression on the right side as functions on the same axes. Finding the x-coordinates of the points of intersection are the solutions to the quadratic equation.

– 

Any quadratic equation, can have zero, one, or two real roots. This is because a parabola can intersect the x-axis in zero, one, or two places.

1.5 Sketch the graph of a quadratic function.

1.6 Solve a contextual problem that involves the characteristics of a quadratic function.

2.1 Determine, with or without technology, the intercepts of the graph of a quadratic function.

2.4 Explain the relationships among the roots of an equation, the zeros of the corresponding function, and the x-intercepts of the graph of the function.

2.5 Explain, using examples, why the graph of a quadratic function may have zero, one or two x-intercepts.

2.7 Solve a contextual problem by modelling a situation with a quadratic equation and solving the equation.

Pages 402 - 403

Questions #5c, 5d, 6c, 8b, 9, 10 and 12

Resources:

Steps to the Graphing Calculator for both Methods

http://mathbits.com/mathbits/tisection/Algebra2/quadraticequations.htm

Purplemath: Solving Quadratic Equations: Solving “by Graphing”

http://www.purplemath.com/modules/solvquad5.htm

YouTube Video: Solving Quadratic Equations Using a Graphing Calculator: Part 1

http://www.youtube.com/watch?v=_VyWTUDJU4c

YouTube Video: Solving Quadratic Equations Using a Graphing Calculator: Example 3

http://www.youtube.com/watch?v=Qhk9QVdnUVQ&feature=related

YouTube Video: Solving Quadratic Equations Using a Graphing Part 1

http://www.youtube.com/watch?v=X6ILUqIc22U&feature=related

ExploreLearning: Roots of a Quadratic

http://www.explorelearning.com/index.cfm?method=cResource.dspView&ResourceID=154&ClassID=135423

Main Concepts in Lesson:

Achievement Indicator:

AFL's Assigned to Assess

To factor an equation, start by writing the equation in standard form.

You can set each factor equal to zero and solve the resulting linear equations. Each solution is a solution to the original equation.

If the two roots of a quadratic equation are equal, then the quadratic equation is said to have one solution.

2.2 Determine, by factoring, the roots of a quadratic equation, and verify by substitution.

2.6 Express a quadratic equation in factored form, given the zeros of the corresponding quadratic function or the x-intercepts of the graph of the function.

2.7 Solve a contextual problem by modelling a situation with a quadratic equation and solving the equation.

Pages 411 - 413

Questions #3b, 3d, 4b, 6a, 7, 9 and 11

Resources:

Brightstorm Video: Solving Quadratic Equations by Factoring

http://www.brightstorm.com/math/algebra/quadratic-equations-and-functions/solving-quadratic-equations-by-factoring/

Purplemath: Solving Quadratic Equations: Solving by Factoring

http://www.purplemath.com/modules/solvquad.htm

ExploreLearning: Quadratic in Factored Form

http://www.explorelearning.com/index.cfm?method=cResource.dspView&ResourceID=115&ClassID=135423

Main Concepts in Lesson:

Achievement Indicator:

AFL's Assigned to Assess

The quadratic formula is used to solve any quadratic equation, even if the equation is not factorable.

If the radicand in the quadratic formula simplifies to a negative number, then there is no real solution for the quadratic equation, therefore, the graph does not cross the x-axis.

2.3 Determine, using the quadratic formula, the roots of a quadratic equation.

2.7 Solve a contextual problem by modelling a situation with a quadratic equation and solving the equation.

Pages 420 - 421

Questions #4c, 4d, 6c, 6d, 9 and 10

Brightstorm Video: The Quadratic Formula

http://www.brightstorm.com/math/algebra/quadratic-equations-and-functions/the-quadratic-formula/

Purplemath: Solving Quadratic Equations: Solving With the Quadratic Formula

http://www.purplemath.com/modules/solvquad4.htm

Main Concepts in Lesson:

Achievement Indicator:

AFL's Assigned to Assess

A function, a graph, or a table of values can represent a relation. Use the form that is most helpful for the context of the problem.

• Depending on the information that is given in a problem, you can use a quadratic function in vertex form or in standard form to model the situation.

Need to Know

• A problem may have only one admissible solution, even though the quadratic equation that is used to represent the problem has two real solutions. When you solve a quadratic equation, verify that your solutions make sense in the context of the problem.

1.1 Determine, with or without technology, the coordinates of the vertex of the graph of a quadratic function.

1.6 Solve a contextual problem that involves the characteristics of a quadratic function.

2.1 Determine, with or without technology, the intercepts of the graph of a quadratic function.

2.2 Determine, by factoring, the roots of a quadratic equation, and verify by substitution.

2.3 Determine, using the quadratic formula, the roots of a quadratic equation.

2.7 Solve a contextual problem by modelling a situation with a quadratic equation and solving the equation.

Pages 430 - 431

Questions #2, 7, and 8

Resources:

Brighstorm Video: Quadratic Equation Applications

http://www.brightstorm.com/math/algebra/quadratic-equations-and-functions/applications-of-quadratic-equations/