Bellwork Find each product. 1. (x+2)(x+9) 2. (5+x)(7-4x) Solve the inequality: 3.

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Bellwork Find each product. 1. (x+2)(x+9) 2. (5+x)(7-4x) Solve the inequality: 3.

Lesson 5.1 Introduction to Quadratic Functions

Why?  Many real-world situations, such as the total stopping distance for a car can be modeled by quadratic functions.

Key Concepts:  Identify a quadratic  Foil to identify the coefficients in a quadratic  Graph quadratics using a calculator  Identify the Vertex, Axis of Symmetry, Domain and Range of a quadratic function

Notes on Lesson 5.1 Introduction to Quadratic Functions A QUADRATIC FUNCTION is any function that can be written in the form ax² + bx +c. EXAMPLE Show that f represents a quadratic function. Identify a, b, and c. f(x) = (2x-1)(3x+5) f(x) = (4-2x)(3-x) a = 6, b = 7, c = -5a = 2, b = -10, c = 12

#1 f(x) = -2x + 6x² #2 f(x) = 24 – 3x #3 f(x) = (3-x)(1+x) #4 f(x) = 6x³ - 8x² 2x

The graph of a quadratic function is a called a parabola. (U) Terms: Axis of symmetry – is a line that divides the parabola into two parts. Vertex of a Parabola – is either the lowest or the highest point on the graph. The domain is the set of all real numbers. The range is either greater than or equal to the min value or less than or equal to the max value.

Parts of a parabola:

Identify the vertex, axis of symmetry, domain and range:

Let’s use our calculators to:  Graph the parabola  Calculate the vertex

Graph the Quadratic Function and give the approximate coordinates for the vertex.  f(x) = -x² +2x - 3

Graph on the calculator and find the vertex, axis of symmetry, domain and range:

Practice:  State whether the parabola opens up or down and whether the y-coordinate of the vertex is the minimum value or the maximum value of the function. Then, give the approximate coordinates for the vertex.  #1 -2x² -2x  #2 (x-2)(x+1)  #3 2+3x+x²

Review:  Identify a quadratic  Foil to identify the coefficients in a quadratic  Graph quadratics using a calculator  Identify the Vertex, Axis of Symmetry, Domain and Range of a quadratic function Tomorrow we graph with no calculator!!

Lesson5.1 Pg every other even