4.6 part 1 notes - graphing quadratic inequalities
TRANSCRIPT
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