5.7 Graphs of Quadratic Inequalities p. 271

Forms of Quadratic Inequalities y<ax 2 +bx+cy>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 < or >, 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 2 +6(0)-4 0≤-4 So, shade where the point is NOT! Test point

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

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