9.7 Graphs of Quadratic Inequalities p. 548

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)

Steps for Graphing (quickly) 1.Complete the data table to get all 5 points 2.Graph the vertex 3.Graph all other 4 points 4.For use DASHED for ≤ or ≥ use SOLID line 5.Shade the appropriate region (“greater than” shade above the vertex, “less than” shade below the vertex)

Shading

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

Graph: y ≤ x 2 + 6x – 4 * Vertex: (-3,-13) * Solid Line * Less than means shade BELOW x = -5, -4, -3, -2, -1

Graph: y > -x 2 + 4x – 3 * Vertex: (2, 1) * Dashed Line * Greater than means shade ABOVE x = 0, 1, 2, 3, 4

Graph: y ≥ x 2 – 8x + 12 * Vertex: (4, -4) * Solid Line * Greater than means shade ABOVE x = 2, 3, 4, 5, 6

Graph: y > -x 2 + 4x + 5 * Vertex: (2, 9) * Dashed Line * Greater than means shade ABOVE x = 0, 1, 2, 3, 4

Assignment