ALGEBRA TWO CHAPTER FIVE QUADRATIC FUNCTIONS SECTION SEVEN Graphs of Quadratic Inequalities

LEARNING GOALS 1. G raph Quadratic Inequalities in two variables. 1. S olve Quadratic inequalities in one variable.

Forms of Quadratic Inequalities Forms of Quadratic Inequalities y ax 2 + bx + c y ≤ ax 2 + bx + cy ≥ ax 2 + bx + c Graphs will look like a parabola with a solid or dotted line and a shaded section. The graph could be shaded inside the parabola or outside.

Steps for graphing 1. Sketch the parabola y=ax 2 +bx+c (dotted line for, solid line for ≤ or ≥) ** remember to use 5 points for the graph! 2. Choose a test point and see whether it is a solution of the inequality. 3. Shade the appropriate region. (if the point is a solution, shade where the point is, if it’s not a solution, shade the other region)

Example: Graph y ≤ x 2 + 6x - 4 * Vertex: (-3, -13) * Opens up, solid line Test Point: (0,0) 0 ≤ (0) ≤ -4 So, shade where the point is NOT! Test point

Graph: y > -x 2 + 4x - 3 * Opens down, dotted line. * Test point (0,0) 0 > (0) > -3 x y Test Point * Vertex: (2,1)

Last Example! Sketch the intersection of the given inequalities. 1. y ≥ x 2 and 2. y ≤ -x 2 + 2x + 4 Graph both on the same coordinate plane. The place where the shadings overlap is the solution. Vertex of #1: (0,0) Other points: (-2,4), (-1,1), (1,1), (2,4) Vertex of #2: (1,5) Other points: (-1,1), (0,4), (2,4), (3,1) * Test point (1,0): doesn’t work in #1, works in #2. SOLUTION!

ASSIGNMENT SECTION 5.7 – pg ; #17, 19, 21, 29, 31, 35, 37, 41, 43, and 45.