Unit 6 Lesson 6 Identify types of Graphs

Unit 6, Lesson 6 Identify types of Graphs Standard: AF 3. 1 Objective: Identify linear, quadratic, and cubic equations based on their graphs.

Proportional vs. Not Proportional • Proportional – Graphs with a constant ratio – Have a pattern – Increase or decrease at a constant – LINES • Not Proportional – Graphs with no constant ratio – May not have a pattern – OTHER SHAPES

Identify Proportional Relationships

1) Linear Equations & Graphs • A linear equation has a regular x value. • A linear graph is a straight line. • The line can go in any direction on the graph.

1) Linear Equations & Graphs • Forms: y = +mx + b Positive Linear y = -mx + b Negative Linear

2) Quadratic Equations & Graphs • A quadratic equation has an x 2 value. • A quadratic graph forms a U shape called a parabola. • The U shape (parabola) can open up or down.

2) Quadratic Equations & Graphs • Forms: y = +Ax 2 • UP is positive • Positive Quadratic y = - Ax 2 • Down is negative • Negative Quadratic

2) Quadratic Equations & Graphs • Let’s see how this works. – Pick some values for x (keep it small to make it easier) X Y – Solve for y. • Example: y = 2 x 2 -2 -1 0 1 2

3) Cubic Equations & Graphs • A cubic equation has an x 3 value. • A cubic graph makes a “s” shape. • A positive x 3 starts down, then goes up. • A negative x 3 starts up, then does down.

3) Cubic Equations & Graphs • Forms: y = +Ax 3 • Increases • Positive Cubic y = -Ax 3 • Decreases • Negative Cubic

3) Cubic Equations & Graphs • Let’s see how this works. – Pick some values for x (keep it small to make it easier) X Y – Solve for y. • Example: y = x 3 -2 -1 0 1 2

Quick Draw for Points! • Now it is time to see if you can remember the shape of each graph. • You will have 30 seconds to draw each graph. • Do your best!

Problem #1 • Draw a positive quadratic graph.

Problem #2 • Draw a linear graph.

Problem #3 • Draw a negative cubic graph.

Problem #4 • Draw a negative quadratic graph.

Problem #5 • Draw a positive cubic graph.

Problem #6 • Write the two forms for a linear equation.

Problem #7 • Write the two forms for a quadratic equation.

Problem #8 • Write the two forms for a cubic equation.