4.6 Part 2 NOTES Graphing Systems of Quadratic Inequalities BELLWORK: Graph the system of linear inequalities. y <2x ‑3 y ≤‑ x +7 LESSON 4.6 PART 2 - Graphing Systems of Quadratic Inequalities • Today we will be graphing SYSTEMS OF QUADRATIC INEQUALITIES . • These are a combination of what weʹve done so far this chapter (graphing parabolas) PLUS what we did last chapter (graphing multiple lines and shading on one side, and where the shaded regions overlap is the answer). STEP 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 of each quadratic inequality is the shaded region. The solution of the SYSTEM of quadratic inequalities is the region where the shaded areas of each quadratic inequality overlap. HOW TO GRAPH SYSTEMS OF QUADRATIC INEQUALITIES Graph the system of quadratic inequalities. y ≥ 2(x + 5) 2 ‑7 y <‑ x 2 ‑2x +5 Graph the system of quadratic inequalities. y> 4x 2 ‑ 40x + 91 y ≤ (x ‑ 5) 2 ‑1
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4.6 Part 2 NOTES Graphing Systems of Quadratic Inequalities
BELLWORK: Graph the system of linear inequalities.
y < 2x ‑ 3
y ≤ ‑ x + 7
LESSON 4.6 PART 2 - Graphing Systems of Quadratic Inequalities
• Today we will be graphing SYSTEMS OF QUADRATIC INEQUALITIES.
• These are a combination of what weʹve done so far this chapter (graphing parabolas) PLUS what we did last chapter (graphing multiple lines and shading on one side, and where the shaded regions overlap is the answer).
STEP 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 of each quadratic inequality is the shaded region. The solution of the SYSTEM of quadratic inequalities is the region where the shaded areas of each quadratic inequality overlap.
HOW TO GRAPH SYSTEMS OF QUADRATIC INEQUALITIES
Graph the system of quadratic inequalities.
y ≥ 2(x + 5)2 ‑ 7
y < ‑ x2 ‑ 2x + 5
Graph the system of quadratic inequalities.
y > 4x2 ‑ 40x + 91
y ≤ (x ‑ 5)2 ‑ 1
4.6 Part 2 NOTES Graphing Systems of Quadratic Inequalities
Graph the system of quadratic inequalities.
y > 2(x + 3)2 ‑ 4
y ≤ ‑(x ‑ 4)(x ‑ 8)
no solution
Graph the system of quadratic inequalities.
y ≤ ‑ (x ‑ 3)(x ‑ 7)
y < ‑ (x + 2)2 + 3
HOMEWORK:4.6 Part 2 Worksheet ‑ Graphing Systems of Quadratic Inequalities
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