Bellwork 1.Solve the inequality and Graph the solution 2.Write a standard form of equation of the line desired Through ( 3, 4), perpendicular to y = - 2x - 4

Section 8.1

Essential Question

What You Will Learn

 A quadratic function is a nonlinear function that can be written in the standard form y = ax 2 + bx + c, where a ≠ 0.  The U-shaped graph of a quadratic function is called a parabola.  In this lesson, you will graph quadratic functions, where b and c equal 0.

Identifying Characteristics of a Quadratic Function  Using the graph, you can identify characteristics such as the vertex, axis of symmetry, and the behavior of the graph, as shown.  You can also determine the following:  The domain is all real numbers.  The range is all real numbers greater than or equal to −2.  When x < −1, y increases as x decreases.  When x > −1, y increases as x increases.

Bellwork 1.These are the center of measures from the last test of your class. Please draw a Box and Whisker plot using this data. Determine whether each relation is a function and what is the domain and range of these functions 2. {(2, 3), (3, 0), (5, 2), (4, 3)} 3. 4.

Identify the vertex, axis of symmetry, and the behavior of the graph,

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Step 1 Make a table of values. Step 2 Plot the ordered pairs. Step 3 Draw a smooth curve through the points. Both graphs open up and have the same vertex, (0, 0), and the same axis of symmetry, x = 0. The graph of g is narrower than the graph of f because the graph of g is a vertical stretch by a factor of 2 of the graph of f

Graph the function. Compare the graph to the graph of f (x) = x2.

Step 1 Make a table of values. Step 2 Plot the ordered pairs. Step 3 Draw a smooth curve through the points. The graphs have the same vertex, (0, 0), and the same axis of symmetry, x = 0, but the graph of h opens down and is wider than the graph of f. So, the graph of h is a vertical shrink by a factor of 1 /3 and a reflection in the x-axis of the graph of f(x)=x2

Graph the function. Compare the graph to the graph of f(x) = x2.

Bellwork 1. Compare the center of measures and standard Deviation of the three classes Find The Difference: Multiply (2u + 1) (4u – 3)

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Step 1 Make a table of values. Step 2 Plot the ordered pairs. Step 3 Draw a smooth curve through the points. Both graphs open up and have the same axis of symmetry, x = 0. The graph of g is narrower, and its vertex, (0, 1), is above the vertex of the graph of f, (0, 0). So, the graph of g is a vertical stretch by a factor of 4 and a vertical translation 1 unit up of the graph of f. Bellwork

The function g is of the form y = f (x) + k, where k = −7. So, the graph of g is a vertical translation 7 units down of the graph of f

A zero of a function f is an x-value for which f(x) = 0. A zero of a function is an x-intercept of the graph of the function.