Lesson 9 Exploring Graphs of Quadratic Functions
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1 Exploring Graphs of Quadratic Functions Graph the following system of linear inequalities: { y > 1 2 x 5 3x + 2y 14 a What are three points that are solutions to the system of inequalities? b Is the point (4, 3) a solution to the system of equations? Explain your answer
2 Exploring Graphs of Quadratic Functions Learning Target I can identify the elements of the quadratic functions QUADRATIC FUNCTIONS Any function that can be placed in the form: f(x) = ax 2 + bx + c, where a 0, but b and c can be zero Opening Activity Read the definition above for quadratic functions and answer the following questions (a) Why is it important for the leading coefficient? to be nonzero? (b) Circle the choices below that are quadratic functions Quadratics still behave in similar ways to other functions Inputs go in, outputs come out But, they start to behave differently from linear and exponential functions because sometimes outputs repeat for quadratics Example 1 Consider the simplest of all quadratic functions, f(x) = x 2 (a) Fill out the table below without using your calculator (b) Graph the function on the grid shown (c) What is the range of this quadratic function?
3 Example 2 Consider the quadratic function y = x 2 2x + 8 (a) Using your calculator to help generate a table (b) Graph this parabola on the grid given (b) State the coordinates of the parabola s turning point (also known as its vertex and its minimum point) (c) State the range of this function (d) Draw the axis of symmetry of the parabola and write its equation below and on the graph (e) State the coordinates of the parabola s turning point (also known as its vertex and its minimum point) (f) What are the x-intercepts of this function? These are also known as the function s zeroes Example 3 f(x) = x 2 4x + 2 is graphed to the left Write the equation of axis of symmetry Identify the turning point vertex
4 Example 4 The quadratic function f x has selected values shown in the table below (a) What are the coordinates of the turning point? (b) What is the range of the quadratic function? Example 5 f(x) = x 2 4x is graphed at right Write the equation of axis of symmetry Find/ identify the vertex Find the x-intercepts or zeros Example 6 Use your graphing calculator with a STANDARD WINDOW to sketch each of the following y = 2x 2 y = 2x 2 End Behavior of the Graph: The graph of the quadratic function is called parabola Given the quadratic function in the form f(x) = ax 2 + bx + c we can say: The graph of quadratic function will open up or concave up, in other words This quadratic function will have a at the x- coordinate of the vertex The graph of quadratic function will open down or concave down, in other words This quadratic function will have a at the x coordinate of the vertex
5 Exploring Graphs of Quadratic Functions Problem Set 1 f(x) = x 2 4x f(x) = x 2 4x Write the equation of axis of symmetry x = Identify the vertex: Identify the x-intercepts: Write the equation of axis of symmetry x = Identify the vertex: Identify the x-intercepts: 3 Write the equation of axis of symmetry Identify the vertex: Identify y-intercept: Identify x-intercepts: 4
6 5 6 7
7 What is the equation of the axis of symmetry of y = x 2 + 2x 7? 13 Will the graph of the parabola y = 2x 2 + 4x 4 open concave up or concave down? Explain how you know your answer 14 Find the y-intercept(s), if any for the equations below: a y = 3x b y = x 2 16
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