1. Modeling Data With Quadratic Functions
ALGEBRA 2 LESSON 5-1
Algebra 2
Lesson 5-1
(Page 234)
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2. Modeling Data With Quadratic Functions
ALGEBRA 2 LESSON 5-1 1
To identify quadratic functions and graphs.
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3. Modeling Data With Quadratic Functions
ALGEBRA 2 LESSON 5-1
New Vocabulary
A quadratic function is a function that
can be written in the standard form:
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4. Modeling Data With Quadratic Functions
ALGEBRA 2 LESSON 5-1
New Vocabulary
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5. Modeling Data With Quadratic Functions
ALGEBRA 2 LESSON 5-1
Classifying Functions
Determine whether each function is linear or quadratic. Identify the quadratic, linear, and constant terms.
a. ƒ(x) = (2x – 1)2
= (2x – 1)(2x – 1)
Multiply.
= 4x2 – 4x + 1
Write in standard form.
This is a quadratic function.
Quadratic term: 4x2
Linear term: –4x
Constant term: 1
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6. Modeling Data With Quadratic Functions
ALGEBRA 2 LESSON 5-1
Classifying Functions
(continued)
b. ƒ(x) = x2 – (x + 1)(x – 1)
= x2 – (x2 – 1)
Multiply.
= 1
Write in standard form.
This is a linear function.
Quadratic term: none
Linear term: 0x (or 0)
Constant term: 1
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7. Modeling Data With Quadratic Functions
ALGEBRA 2 LESSON 5-1
Classifying Functions
Determine whether each function is linear or quadratic. Identify the quadratic, linear, and constant terms.
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8. Modeling Data With Quadratic Functions
ALGEBRA 2 LESSON 5-1
New Vocabulary
The graph of a quadratic function
is a parabola.
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9. Modeling Data With Quadratic Functions
ALGEBRA 2 LESSON 5-1
New Vocabulary
The axis of symmetry is the line that
divides a parabola into two parts that
are mirror images.
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10. Modeling Data With Quadratic Functions
ALGEBRA 2 LESSON 5-1
New Vocabulary
The vertex of a parabola is the point at
which the parabola intersects the
axis of symmetry.
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11. Modeling Data With Quadratic Functions
ALGEBRA 2 LESSON 5-1
Points on a Parabola
Below is the graph of y = x2 – 6x Identify the vertex and the axis of symmetry. Identify points corresponding to P and Q.
The vertex is (3, 2).
The axis of symmetry is x = 3.
P(1, 6) is two units to the left of the axis of symmetry.
Corresponding point P (5, 6) is two units to the right of the axis of symmetry.
Q(4, 3) is one unit to the right of the axis of symmetry.
Corresponding point Q (2, 3) is one unit to the left of the axis of symmetry.
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12. Modeling Data With Quadratic Functions
ALGEBRA 2 LESSON 5-1
Points on a Parabola
Below is the graph of y = x2 – 6x Identify the vertex and the axis of symmetry. Identify points corresponding to P and Q.
  A. (–1, 1); x = –1; P´(–1, 3); Q´(2, 0)
  B. (1, –1); x = 1; P´(3, 3); Q´(0, 0)
  C. (1, 1); y = 1; P´(3, 3); Q´(0, 0)
  D. (–1, 1); y = –1; P´(–1, 3); Q´(2, 0)
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13. Modeling Data With Quadratic Functions
ALGEBRA 2 LESSON 5-1
Points on a Parabola
Below is the graph of y = x2 – 6x Identify the vertex and the axis of symmetry. Identify points corresponding to P and Q.
  A. (–1, 2); x = –1; P´(0, 1); Q´(–3, –2)
  B. (2, 1); x = 2; P´(–2, 1); Q´(1, –2)
  C. (–2, 1); y = 2; P´(0, 1); Q´(–3, –2)
  D. (–1, 2); y = –1; P´(–2, 1); Q´(1, –2)
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14. Modeling Data With Quadratic Functions
ALGEBRA 2 LESSON 5-1
Algebra 2
Lesson 5-1
(Page 234)
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