Graphing Quadratic Inequalities Quadratic Inequalities Decide whether the

Graphing Quadratic Inequalities

Quadratic Inequalities Decide whether the point is a solution of the inequality: y≥ 2 -2 x + 5 x + 7 (-2, 10) Plug in and evaluate 10 ≥ -2(-2)2 + 5(-2) + 7 10 ≥ -2(4) + 5(-2) + 7 10 ≥ -8 – 10 + 7 10 ≥ -11 True. YES (-2, 10) is a solution

Remember how to graph a linear inequality? • Write in slopeintercept form: – – • • Sketch the graph of 6 x + 5 y ≥ 30 y ≥ -6/5 x + 6 This will be a solid line. Test a point. (0, 0) 6(0) + 5(0) ≥ 30 0 ≥ 30 Not a solution. Shade the side that doesn’t include (0, 0). 6 4 2 -6 -4 -2 -2 -4 -6 2 4 6 8

Rules for Graphing Quadratic Inequalities: 1. Sketch the graph of the parabola y<ax 2+bx+c use ------ line for <, > use ______ line for 2. Test points inside the U shape and one outside the U shape. 3. Shade the region that contains the solution.

2 Check discriminant first for number of solutions b 2 -4 ac 2 (-2) -4(3)(4) 4 -48 -44 NO SOLUTION = Quadratic equation won’t work for x-intercepts. (It will be ‘floating above’ the x-axis)

Next Step… y≥ 2 3 x – 2 x + 4 Find axis of symmetry and vertex -b 2 a -(-2) 2∙ 3 2 6 3(1/3)2 – 2(1/3) + 4 3(1/9) – 2/3 + 4 1/ 2/ + 4 – 3 3

Find more points x 3 x 2 – 2 x + 4 y (x, y) -1 3(-1)2– 2(-1) + 4 9 (-1, 9) Vertex 2 (1/3, 32/3) 3(2)2 - 2(2) + 4 12 Now sketch the graph. (2, 12)

y≥ 2 3 x – 2 x + 4 8 6 4 y Solid line 2 -6 -4 -2 -2 -4 -6 -8 2 4 6 8 x

Check Point 2 NO Out In (0, 0) (0, 6) 2 Yes

y Final Graph 2 8 6 4 2 -6 -4 -2 -2 -4 -6 -8 2 4 6 8 x

Try this one • y > -x 2 + 2 x – 1 • Find the vertex (1, 0) • Pick more points • Graph • Shade (pick a test point and shade the true side)

y Shade outside 8 6 4 2 -6 -4 -2 -2 -4 -6 -8 (1, 0) 2 4 6 8 x Dotted line