quadratic functions ticket in the door lesson essential question what are the important parts of a...
TRANSCRIPT
- Slide 1
- Slide 2
- Quadratic Functions
- Slide 3
- Ticket In The Door
- Slide 4
- Lesson Essential Question What are the important parts of a quadratic graph?
- Slide 5
- Quadratic Review For each quadratic function: Identify the quadratic term (a) Identify the linear term (b) Identify the constant term (c)
- Slide 6
- Quadratic Function: y = ax 2 + bx + c Example 1: 2x 2 + 3x + 10a = _____b = _____c = _____ Example 2: -3x 2 + 5x a = _____b = _____c = _____ Example 3: x 2 - 8x + 7a = _____b = _____c = _____ Example 4: -x 2 - 9x 3 a = _____b = _____c = _____ Example 5: -x 2 - 6x a = _____b = _____c = _____ Example 6: x 2 a = _____b = _____c = _____
- Slide 7
- Consider the following quadratic function: f(x) = x 2 + 2x 3 Lets talk about another important part of a quadratic function: Where is the y-intercept? y-intercept: (0, -3) Where does the function cross the y-axis?
- Slide 8
- Consider the following quadratic function: f(x) = x 2 + 2x 3 Lets talk about another important part of a quadratic function: Where are the x- intercepts? x-intercepts: (1, 0) & (-3, 0) Where does the function cross the x-axis?
- Slide 9
- Consider the following quadratic function: f(x) = x 2 + 2x 3 Lets talk about several important parts of a quadratic function: Where is the vertex? (-1, -4)
- Slide 10
- Consider the following quadratic function: f(x) = x 2 + 2x 3 Lets talk about another important part of a quadratic function: How do we algebraically calculate the vertex?
- Slide 11
- Consider the following quadratic function: f(x) = x 2 + 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?
- Slide 12
- Consider the following quadratic function: f(x) = x 2 + 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).
- Slide 13
- Consider the following quadratic function: f(x) = x 2 + 2x 3 Lets 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?
- Slide 14
- Consider the following quadratic function: f(x) = x 2 + 2x 3 Lets talk about another important part of a quadratic function: How do we represent this axis of symmetry? x = -1
- Slide 15
- Consider the following quadratic function: f(x) = x 2 2x 15 Where are the x- intercepts? x-intercepts: (-3, 0) & (5, 0) Where does the function cross the x-axis?
- Slide 16
- Consider the following quadratic function: f(x) = x 2 2x 15 Where is the y-intercept? y-intercept: (0, -15) Where does the function cross the y-axis?
- Slide 17
- Lets Do It Again Ourselves!! Consider the following quadratic function: f(x) = x 2 2x 15 Where is the vertex? Algebraically calculate the vertex. (1, -16)
- Slide 18
- Consider the following quadratic function: f(x) = x 2 2x 15 Where is the axis of symmetry? Draw in the axis of symmetry. What is the axis of symmetry?
- Slide 19
- Consider the following quadratic function: f(x) = x 2 + 3x Where is the y-intercept? y-intercept: (0, 0) Where does the function cross the y-axis?
- Slide 20
- Consider the following quadratic function: f(x) = x 2 + 3x Where are the x- intercepts? x-intercepts: (-3, 0) & (0, 0) Where does the function cross the x-axis?
- Slide 21
- Lets Do It Again Ourselves!! Consider the following quadratic function: f(x) = x 2 + 3x Where is the vertex? Algebraically calculate the vertex. (-1.5, -2.25)
- Slide 22
- Consider the following quadratic function: f(x) = x 2 + 3x Where is the axis of symmetry? Draw in the axis of symmetry. What is the axis of symmetry?
- Slide 23
- Now, Visualize the graph! Given: f(x) = x 2 4x + 3 Open up or down? Calculate the vertex? What is the axis of symmetry? Where is the y-intercept?
- Slide 24
- Now, Visualize the graph! Given: f(x) = 2x 2 + 3x 1 Open up or down? Calculate the vertex? What is the axis of symmetry? Where is the y-intercept?
- Slide 25
- Now, Visualize the graph! Given: f(x) = 5x 2 2x + 5 Open up or down? Calculate the vertex? What is the axis of symmetry? Where is the y-intercept?
- Slide 26
- Now, Visualize the graph! Given: f(x) = x 2 2x 15 Open up or down? Calculate the vertex? What is the axis of symmetry? Where is the y-intercept?
- Slide 27
- Ticket Out The Door 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.
- Slide 28
- 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)
- Slide 29
- Quadratic Functions and their important parts! What important parts do you recognize in this graph? y = x 2 3x 10
- Slide 30
- Quadratic Functions and their important parts! What important parts do you recognize in this graph?
- Slide 31
- Lesson Essential Question How do you graph a quadratic function using the vertex?
- Slide 32
- 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
- Slide 33
- Calculate the vertex and identify the axis of symmetry (AOS).
- Slide 34
- Graphing Quadratic Functions Graph the function, then identify the x-intercepts (roots) = ____________
- Slide 35
- Graphing Quadratic Functions Graph the function, then identify the x-intercepts (roots) = ____________
- Slide 36
- Graphing Quadratic Functions Graph the function, then identify the x-intercepts (roots) = ____________
- Slide 37
- Graphing Quadratic Functions Graph the function, then identify the x-intercepts (roots) = ____________
- Slide 38
- Graphing Quadratic Functions e.) Sketch the graph of y = x 2 2x 3 Graph the function, then identify the x-intercepts (roots) = ____________
- Slide 39
- Graphing Quadratic Functions f.) Sketch the graph of y = x 2 + 4x + 4 Graph the function, then identify the x-intercepts (roots) = ____________
- Slide 40
- Graphing Quadratic Functions g.) Sketch the graph of y = x 2 3 Graph the function, then identify the x-intercepts (roots) = ____________
- Slide 41
- Graphing Quadratic Functions h.) Sketch the graph of y = 2x 2 + 4x + 5 Graph the function, then identify the x-intercepts (roots) = ____________
- Slide 42
- On Your Own Practice Please complete the practice worksheets in order to develop and master this skill. Thank you
- Slide 43
- Homework Assignment More Practice Graphing Quadratic Functions!