unit 10 quadratic functions
Download
Skip this Video
Download Presentation
Unit 10 – Quadratic Functions

Loading in 2 Seconds...

play fullscreen
1 / 17

Unit 10 – Quadratic Functions - PowerPoint PPT Presentation


  • 149 Views
  • Uploaded on

Unit 10 – Quadratic Functions. Topic: Characteristics of Quadratic Functions. What is a quadratic function?. Standard form: Parent quadratic function: Graph: parabola. What is the vertex of a quadratic function?. Highest or lowest point Vertex: (-1, -6) y -value is called minimum

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about ' Unit 10 – Quadratic Functions' - crevan


An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
unit 10 quadratic functions

Unit 10 – Quadratic Functions

Topic: Characteristics of Quadratic Functions

what is a quadratic function
What is a quadratic function?
  • Standard form:
  • Parent quadratic function:
  • Graph: parabola
what is the vertex of a quadratic function
What is the vertex of a quadratic function?
  • Highest or lowest point
  • Vertex: (-1, -6)
    • y-value is called minimum
    • Parabola opens upward (a > 0)
what is the vertex of a quadratic function1
What is the vertex of a quadratic function?
  • Vertex: (1, 7)
    • y-value is called maximum
    • Parabola opens downward (a < 0)
finding domain range
Finding domain & range
  • Domain: ALWAYS all real #
  • Range: ALWAYS an inequality
    • y coordinate of vertex represents minimum or maximum value of range
  • Range: y ≥ -6
finding domain range1
Finding domain & range
  • Domain: all real #
  • Range: y ≤ 7
what is the axis of symmetry
What is the axis of symmetry?
  • Vertical line that divides parabola in half
    • REMEMBER: equation for a vertical line is x = a
  • a of s: x = -1
finding axis of symmetry algebraically
Finding axis of symmetry algebraically
  • Formula:
  • Example: Find the axis of symmetry for the function

Plug in values for a (2) & b (–8) & simplify. WATCH YOUR SIGNS!

Axis of symmetry for this function is the vertical line x = 2. SIGN NOTE: Notice the two negatives cancel. Remember the formula includes a negative.

using axis of symmetry to find vertex
Using axis of symmetry to find vertex
  • Finding vertex coordinates:
    • x-coordinate: axis of symmetry
    • y-coordinate: substitute x-coordinate into function & simplify

We’ve already found the x-coordinate (2). Replace x in the function with 2 & solve for y.

Vertex for this function is the point (2, –11).

what are the zeros of a quadratic function
What are the zeros of a quadratic function?
  • x-value(s) that makes function = 0
  • Using graph: zeros are the points where the parabola crosses x-axis
    • Two real zeros
    • x = -1 and x = 2
determining a function from a graph
Determining a Function From a Graph
  • Identify 3 points from the graph.
    • One should be the y-intercept; pick points that make the math easy.
  • (0, 6), (2, 0), (3, 0)
determining a function from a graph1
Determining a Function From a Graph
  • Using standard form of a quadratic equation, write a system of equations.
    • REMEMBER: We already have a value for c(from y-intercept).
determining a function from a graph2
Determining a Function From a Graph
  • Simplify & solve for a & b.

Divide 1st equation by -2. Divide 2nd equation by 3. Add equations to eliminate b.

Plug the value of a into one of the equations & solve for b.

determining a function from a graph3
Determining a Function From a Graph

Write the function in standard form with the values of a, b & c.

Check your equation on your graphing calculator.

homework

Homework

Complete the handout you received in class. Be prepared to present solutions on the board.

DUE 4/16 (A-day) or 4/17 (B-day)

ad