Modeling Data With Quadratic Functions ALGEBRA 2 LESSON 5-1 Algebra 2 Lesson 5-1 (Page 234) 1-1

Modeling Data With Quadratic Functions ALGEBRA 2 LESSON 5-1 1 To identify quadratic functions and graphs. 1-1

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: 1-1

Modeling Data With Quadratic Functions ALGEBRA 2 LESSON 5-1 New Vocabulary 1-1

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 5-1

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 5-1

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. 5-1

Modeling Data With Quadratic Functions ALGEBRA 2 LESSON 5-1 New Vocabulary The graph of a quadratic function is a parabola. 1-1

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. 1-1

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. 1-1

Modeling Data With Quadratic Functions ALGEBRA 2 LESSON 5-1 Points on a Parabola Below is the graph of y = x2 – 6x + 11. 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. 5-1

Modeling Data With Quadratic Functions ALGEBRA 2 LESSON 5-1 Points on a Parabola Below is the graph of y = x2 – 6x + 11. 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) 5-1

Modeling Data With Quadratic Functions ALGEBRA 2 LESSON 5-1 Points on a Parabola Below is the graph of y = x2 – 6x + 11. 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) 5-1

Modeling Data With Quadratic Functions ALGEBRA 2 LESSON 5-1 Algebra 2 Lesson 5-1 (Page 234) 1-1