12.2 vertex form 2016 ink.notebook
April 28, 2017
Page 167
Page 168
12.2
Completing
the Square Vertex Form
Lesson Objectives
Standards
Lesson 12.2 Completing the Square – Vertex Form
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Lesson Objectives
Standards
Lesson
A.SSE.2
A.SSE.3
A.SSE.3
A.SSE.3 A.REI.4
A.REI.4
F.IF.8
I will rewrite a quadratic function into vertex form by completing the square I will solve a quadratic function by completing the square I will find the maximum or minimum of a quadratic function completing the square I will find the vertex of a quadratic function completing the square I will solve a quadratic equation by completing the square I will using completing the square to put a quadratic function into vertex form I will use completing the square to find the max or min of a quadratic function F.IF.8
I will use completing the square to find the axis of symmetry of a quadratic function Press the tabs to view details.
1
12.2 vertex form 2016 ink.notebook
Lesson Objectives
Standards
Lesson A.REI.4 Solve quadratic equations in one variable.
a) Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x – p)2 = q that has the same solutions.
b) Solve quadratic equations by inspection (e.g., for x2 = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation.
A.SSE.3 Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.
b) Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines.
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April 28, 2017
f(x) = x2 – 10x + 5 1) move the constant to the – 5
– 5
other side & add blanks
–5 + ___ = x2 – 10x + ___ –5 + 25 = x2 – 10x + 25 2) Divide by 2 and square
–10
it to fill in blanks
2
(–5)2
20 = (x – 5)2 3) add or subtract the
-20
-20
constant to the other
2 f(x) = (x – 5) – 20 Vertex: (5, –20)
side
4) Put f(x) back in
Axis of symmetry: x = 5
f(x) = a(x – h) 2 + k,
where (h, k) is the vertex.
Write each quadratic function in vertex form. Give the coordinates of the vertex and the axis of symmetry. 1. f(x) = x2 + 4x
2. f(x) = x2 + 8x + 11
2
12.2 vertex form 2016 ink.notebook
April 28, 2017
Write each quadratic function in vertex form. Give the coordinates of the vertex and the axis of symmetry. 3. f(x) = x2 – 2x – 3 4. g(x) = x2 – 6x – 2 Write each quadratic function in vertex form. Give the coordinates of the vertex and the axis of symmetry. 6. g(x) = x2 – 7x + 3
5. f(x) = x2 + 3x – 4 3
12.2 vertex form 2016 ink.notebook
April 28, 2017
On Your
Whiteboards
Homework
Homework
Hint
On the
Worksheet
Homework
1
4
9
16
25
36
49
64
81
100
121
144
169
196
225
4
12.2 vertex form 2016 ink.notebook
Write each quadratic function in vertex form. Give the coordinates of the vertex and the axis of symmetry. April 28, 2017
2. g(x) = x2 + 4x – 3 1. g(x) = x2 + 6x – 5
3. g(x) = x2 – 8x + 1
4. f(x) = x2 + 2x + 5
5
12.2 vertex form 2016 ink.notebook
5. f(x) = x2 – 3x + 5
7. f(x) = x2 + 4x + 6
April 28, 2017
6. f(x) = x2 – 5x + 10
8. f(x) = x2 – 6x + 7
6
12.2 vertex form 2016 ink.notebook
9. f(x) = x2 – 2x + 4
April 28, 2017
Solve by completing the square. Give exact solutions. SHOW WORK. 10. x2 – 9x = –12
Solve by completing the square. Give exact solutions. SHOW WORK. 12. x + 4x + 2 = 0
2
11. x2 – 2x = 10
Solve each equation. Give the exact answer. SHOW ALL WORK. 13. (x – 9)2 = 144
14. 5(x + 5)2 = 50
7
12.2 vertex form 2016 ink.notebook
Solve each equation. Give the exact answer. SHOW ALL WORK. 15. 3x – 7 = 41
2
April 28, 2017
16. Antonia is carpeting two of the rooms in her house. The dimensions are shown. What is the total area to be carpeted?
a) x2 + 3x
b) x2 + 3x – 5
x - 2
x + 5
c) 2x2 + 6x – 10
d) 8x + 12
x
x + 3
ANSWERS:
8