algebra 2 lesson 5-1 (page 234) algebra 2 lesson 5-1 modeling data with quadratic functions 1-1

Algebra 2Lesson 5-1(Page 234)

ALGEBRA 2 LESSON 5-1ALGEBRA 2 LESSON 5-1

Modeling Data With Quadratic FunctionsModeling Data With Quadratic Functions

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To identify quadratic functions and graphs.



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New Vocabulary

A quadratic function is a function that

can be written in the standard form:

cbxaxxf 2



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New Vocabulary

cbxaxxf 2

Term Quadratic2 ax

TermLinear bx

TermConstant c

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: –4xConstant term: 1

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(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: noneLinear term: 0x (or 0)Constant term: 1

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Determine whether each function is linear or quadratic. Identify the quadratic, linear, and constant terms.



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New Vocabulary

The graph of a quadratic function

is a parabola.



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New Vocabulary

The axis of symmetry is the line that

divides a parabola into two parts that

are mirror images.



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New Vocabulary

The vertex of a parabola is the point at

which the parabola intersects the

axis of symmetry.

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.

Below is the graph of y = x2 – 6x + 11. Identify the vertex and the axis of symmetry. Identify points corresponding to P and Q.



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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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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)

Algebra 2Lesson 5-1(Page 234)



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algebra 2 lesson 5-1 (page 234) algebra 2 lesson 5-1 modeling data with quadratic functions 1-1

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