Lesson 5.8 honors
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This document discusses checking solutions to quadratic inequalities and graphing quadratic inequalities. It provides examples of checking if an ordered pair is a solution to an inequality and finding the vertex of a quadratic function to graph it as a solid curve below or above the vertex based on whether the inequality is ≤ or ≥.
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Okay, let's solve this step-by-step:
1) FOIL the expression: y = 3(x + 2)(x + 2) - 4
= 3(x^2 + 4x + 2x + 4) - 4
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= 3x^2 + 12x + 8
2) This is in the vertex form: y = a(x - h)^2 + k
Where:
a = 3
h = -2
k = 8
So the equation in vertex form is:
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y = 3(x + 2)^2 - 4
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Okay, let's solve this step-by-step:
1) FOIL the expression: y = 3(x + 2)(x + 2) - 4
= 3(x^2 + 4x + 2x + 4) - 4
= 3x^2 + 12x + 12 - 4
= 3x^2 + 12x + 8
2) This is in the vertex form: y = a(x - h)^2 + k
Where: a = 3
h = 0
k = 8
So the equation in vertex form is:
y = 3(x - 0)^2 + 8
Or simply:
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Lesson 5.8 honors
- 1. 5.8 Quadratic Inequalities Checking Solutions Decide whether the ordered pair is a solution, of the inequality. ) x 1 2.− y < 2 (1x + 1 , 2 −1 < 2 + 1 −1 < 3 (1,−1)
- 2. Checking Solutions Decide whether the ordered pair is a solution, of the inequality. (, 3 x 3.− y > 2 − 3 x2 ) ( 2,−3) 2 −3 > 4 −6 − 3 > −2
- 3. Graphing a Quadratic Inequality 4. y ≤ x + 4 x + 4 2 Vertex: 4 4 b =− − 2 1 2 (a ) 2 y = (− 2) + 4( − 2) + 4 y = 4 −8 + 4 = 0 ( − 2, 0 Solid Check (0,0) 0≤4 Normal Graph )
- 4. Graphing a Quadratic Inequality 5. y ≥ 3 x − 12 2 0 0 b =− − 6 3 2 (a ) 2 y = 3( 0 ) − 12 y = 0 − 12 = −12 Check (0,0) 0 ≥ −12 Vertex: ( 0, − 12) Solid
- 5. Graphing a Quadratic Inequality 6. y ≤ x − 10 x + 9 2 Vertex: − 10 10 b = − 2 1 2 (a) 2 y = ( 5 ) − 10( 5 ) + 9 y = 25 − 50 + 9 Check (0,0) 0≤9 ( 5, − 16) Solid
- 6. Graphing a Quadratic Inequality 6. y ≤ x − 10 x + 9 2 Vertex: − 10 10 b = − 2 1 2 (a) 2 y = ( 5 ) − 10( 5 ) + 9 y = 25 − 50 + 9 Check (0,0) 0≤9 ( 5, − 16) Solid