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Quadratic Functions

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Ticket In The Door

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**Lesson Essential Question**

What are the important parts of a quadratic graph?

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**Quadratic Review For each quadratic function:**

Identify the quadratic term (a) Identify the linear term (b) Identify the constant term (c)

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**Quadratic Function: y = ax2 + bx + c**

Example 1: 2x2 + 3x + 10 a = _____ b = _____ c = _____ Example 2: -3x2 + 5x a = _____ b = _____ c = _____ Example 3: x2 - 8x + 7 a = _____ b = _____ c = _____ Example 4: -x2 - 9x – 3 a = _____ b = _____ c = _____ Example 5: -x2 - 6x a = _____ b = _____ c = _____ Example 6: x2 a = _____ b = _____ c = _____

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**Consider the following quadratic function: f(x) = x2 + 2x – 3**

Let’s talk about another important part of a quadratic function: Where is the y-intercept? Where does the function cross the y-axis? y-intercept: (0, -3)

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**Consider the following quadratic function: f(x) = x2 + 2x – 3**

Let’s talk about another important part of a quadratic function: Where are the x-intercepts? Where does the function cross the x-axis? x-intercepts: (1, 0) & (-3, 0)

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**Consider the following quadratic function: f(x) = x2 + 2x – 3**

Let’s talk about several important parts of a quadratic function: Where is the vertex? (-1, -4)

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**Consider the following quadratic function: f(x) = x2 + 2x – 3**

Let’s talk about another important part of a quadratic function: How do we algebraically calculate the vertex?

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**Consider the following quadratic function: f(x) = x2 + 2x – 3**

Calculating the vertex. The vertex is a coordinate point (x, y) on the graph, now that we have the x value how do you think we determine the y value?

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**Consider the following quadratic function: f(x) = x2 + 2x – 3**

Calculating the vertex. Substitute the value of x into the given function equation above and solve! The answer is the value for y. When x = -1, y = -4. Vertex is: (-1, -4).

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**Consider the following quadratic function: f(x) = x2 + 2x – 3**

Let’s talk about another important part of a quadratic function: What is the axis of symmetry? Now that you see what it is, how would you define the axis of symmetry?

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**Consider the following quadratic function: f(x) = x2 + 2x – 3**

Let’s talk about another important part of a quadratic function: How do we represent this axis of symmetry? x = -1

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**Consider the following quadratic function: f(x) = x2 – 2x – 15**

Where are the x-intercepts? Where does the function cross the x-axis? x-intercepts: (-3, 0) & (5, 0)

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**Consider the following quadratic function: f(x) = x2 – 2x – 15**

Where is the y-intercept? Where does the function cross the y-axis? y-intercept: (0, -15)

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**Let’s Do It Again Ourselves**

Let’s Do It Again Ourselves!! Consider the following quadratic function: f(x) = x2 – 2x – 15 Where is the vertex? Algebraically calculate the vertex. (1, -16)

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**Consider the following quadratic function: f(x) = x2 – 2x – 15**

Where is the axis of symmetry? Draw in the axis of symmetry. What is the axis of symmetry?

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**Consider the following quadratic function: f(x) = x2 + 3x**

Where is the y-intercept? Where does the function cross the y-axis? y-intercept: (0, 0)

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**Consider the following quadratic function: f(x) = x2 + 3x**

Where are the x-intercepts? Where does the function cross the x-axis? x-intercepts: (-3, 0) & (0, 0)

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**Let’s Do It Again Ourselves**

Let’s Do It Again Ourselves!! Consider the following quadratic function: f(x) = x2 + 3x Where is the vertex? Algebraically calculate the vertex. (-1.5, -2.25)

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**Consider the following quadratic function: f(x) = x2 + 3x**

Where is the axis of symmetry? Draw in the axis of symmetry. What is the axis of symmetry?

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**Now, Visualize the graph!**

Given: f(x) = x2 – 4x + 3 Open up or down? Calculate the vertex? What is the axis of symmetry? Where is the y-intercept?

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**Now, Visualize the graph!**

Given: f(x) = 2x2 + 3x – 1 Open up or down? Calculate the vertex? What is the axis of symmetry? Where is the y-intercept?

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**Now, Visualize the graph!**

Given: f(x) = 5x2 – 2x + 5 Open up or down? Calculate the vertex? What is the axis of symmetry? Where is the y-intercept?

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**Now, Visualize the graph!**

Given: f(x) = x2 – 2x – 15 Open up or down? Calculate the vertex? What is the axis of symmetry? Where is the y-intercept?

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**Ticket Out The Door Homework**

Complete the ticket out the door problem. Please hand it to me as you walk out of the door. Homework Complete the worksheet for homework.

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**IMPORTANT PARTS OF QUADRATIC GRAPHS**

Does the graph open up or down (write “a” is + or -) Put a star at the Vertex (write the point) Draw the Axis of Symmetry and write the equation Circle the X-intercepts (write the point) Draw a square around the Y-intercept (write the point)

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**Quadratic Functions and their important parts!**

What important parts do you recognize in this graph? y = x2 – 3x – 10

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**Quadratic Functions and their important parts!**

What important parts do you recognize in this graph?

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**Lesson Essential Question**

How do you graph a quadratic function using the vertex?

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**Putting It All Together Now!!!**

Graphing Parabolas In order to graph we will need the following: Visualize whether the parabola open up or down Calculate the coordinates of the Vertex Determine the Axis of Symmetry Determine the y-intercept Plot a few more points to understand the actual shape of the graph Identify the x-intercepts

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**Calculate the vertex and identify the axis of symmetry (AOS).**

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**Graphing Quadratic Functions**

Graph the function, then identify the x-intercepts (roots) = ____________

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**Graphing Quadratic Functions**

Graph the function, then identify the x-intercepts (roots) = ____________

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**Graphing Quadratic Functions**

Graph the function, then identify the x-intercepts (roots) = ____________

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**Graphing Quadratic Functions**

Graph the function, then identify the x-intercepts (roots) = ____________

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**Graphing Quadratic Functions**

e.) Sketch the graph of y = x2 – 2x – 3 Graph the function, then identify the x-intercepts (roots) = ____________

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**Graphing Quadratic Functions**

f.) Sketch the graph of y = x2 + 4x + 4 Graph the function, then identify the x-intercepts (roots) = ____________

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**Graphing Quadratic Functions**

g.) Sketch the graph of y = ½x2 – 3 Graph the function, then identify the x-intercepts (roots) = ____________

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**Graphing Quadratic Functions**

h.) Sketch the graph of y = 2x2 + 4x + 5 Graph the function, then identify the x-intercepts (roots) = ____________

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On Your Own Practice Please complete the practice worksheets in order to develop and master this skill. Thank you

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**More Practice Graphing Quadratic Functions!**

Homework Assignment More Practice Graphing Quadratic Functions!

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