4.6 Part 1 NOTES ­ Graphing Quadratic Inequalities

BELLWORK #1: Identify which form each quadratic equation is written in.

A)  y = 2(x ‑ 1)2 + 7

B)  y = ‑    (x ‑ 4)(x + 8)

C)  y = 3x2

D)  y = ‑x2 + 9x + 10

Vertex

Standard

Standard (Basic)

Intercept

BELLWORK #2: Graph the linear inequality.

  y < 2x ‑ 30 < -3 ?false

Shade away from (0, 0)

LESSON 4.6 - Graphing Quadratic Inequalities

• Today we will be graphing QUADRATIC INEQUALITIES.

• These are a combination of what weʹve done so far this chapter (graphing parabolas) PLUS what we did last chapter (graphing lines and shading on one side).

HOW TO GRAPH QUADRATIC INEQUALITIESSTEP 1:  Graph the parabolas like you normally would

• Use a solid curve for ≤ and ≥

• Use a dotted curve for < and >

STEP 2:  Plug the point (0, 0) into the original inequality to see if it gives you a true statement.

• If it does give you a true statement, shade where (0, 0) is

• If it gives you a false statement, shade where (0, 0) is not

NOTE: If the parabola passes through the point (0, 0), then you must pick a different point to plug in.

STEP 3:  The solution is the area that you shade.

Graph the quadratic inequality.

  y ≥ (x + 3)2 ‑ 2

0 ≥ (0 + 3)2 - 2 ?0 ≥ 7 ?false

Shade away from (0, 0)

4.6 Part 1 NOTES ­ Graphing Quadratic Inequalities

Graph the quadratic inequality.

y > ‑   (x ‑ 6)(x + 2)

0 > - (0 - 6)(0 + 2) ?0 > 1.5 false

Shade away from (0, 0)

12

Graph the quadratic inequality.

  y > 3x2 ‑ 6x ‑ 5

0 > 3(0)2 - 6(0) - 5 ?0 > -5 ?true

Shade toward (0, 0)

Graph the quadratic inequality.

  y ≥ ‑   x2

Passes through (0, 0), must pick a different point: (1, 1)

1 > - (1)2

1 > - true

Shade toward (1, 1)

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HOMEWORK:4.6 Part 1 Worksheet ‑ Graphing Quadratic Inequalities