Quadratic Functions

Ticket In The Door

Lesson Essential Question What are the important parts of a quadratic graph?

Quadratic Review For each quadratic function: Identify the quadratic term (a) Identify the linear term (b) Identify the constant term (c)

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 = _____

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)

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)

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)

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?

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?

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).

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?

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

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)

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)

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)

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?

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)

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)

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)

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?

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?

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?

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?

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?

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.

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)

Quadratic Functions and their important parts! What important parts do you recognize in this graph? y = x2 – 3x – 10

Quadratic Functions and their important parts! What important parts do you recognize in this graph?

Lesson Essential Question How do you graph a quadratic function using the vertex?

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

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

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

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

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

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

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

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

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

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

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

More Practice Graphing Quadratic Functions! Homework Assignment More Practice Graphing Quadratic Functions!