Unit 10 quadratic functions
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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

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Unit 10 – Quadratic Functions

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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


What are the zeros of a quadratic function1

What are the zeros of a quadratic function?

  • one real zero

    • x = 1


What are the zeros of a quadratic function2

What are the zeros of a quadratic function?

  • No real zeros


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)


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