5-1 Modeling Data with Quadratic Functions I can: Determine whether an equation is linear or...

5-1 Modeling Data with Quadratic Functions

I can:• Determine whether an

equation is linear or quadratic.

• Identify the axis of symmetry from a given graph.

• Identify the axis of symmetry from a given equation.

• Identify the vertex of the parabola from a given graph.

• Identify the vertex of the parabola from an equation.

Quadratic Function A function that can be written in the form

where . Domain of a quadratic function

All Real Numbers

Quadratic Term Linear Term Constant Term

Example 1: Are the following functions quadratic?

a) b)

Graphs of Quadratic Functions Graph is a parabola.

Vertex is the point at which the parabola intersects the axis of symmetry.

Y-value of the vertex of a parabola represents the max or min value of the function.

Axis of symmetry – line that divides a parabola into two parts that are mirror images. Defined by the x-coordinate of the vertex.

5-2 Properties of Parabolas

I can:• Graph a quadratic

function of the form • Graph a quadratic

function of the form • Find maximum and

minimum value of a quadratic function.

Graph of a Quadratic Function in Standard Form When , the parabola opens up. When the parabola opens down. x-coordinate of the vertex: Axis of symmetry: Or we can put it in Vertex form…

y-coordinate: plug in x-value or ) y-intercept: Stretch Shrink

Example 1: Grapha)

Trivia…1. While working in a resort for the winter season, the caretaker becomes possessed by the spirits haunting the establishment. What book and movie plot is this?

The Shining

2. An elderly woman recounts her life and falling in love on an extravagant cruiseliner during the early 1900's. What movie plot is this? Titanic

3. A cowboy helps 'another of his kind' realize that his aspirations of being a true space ranger is not his destiny. What movie plot is this?

Toy Story

Example 1: Graphb)

You try…c)

Example 1: Graphd)

Example 2: Find a quadratic function that includes the values in the tables.

x y

-2 -17

1 10

5 -10

You try...

x y

1 0

2 -3

3 -10

Max & Min y-coordinate of the vertex of a parabola

represents the max or min of a quadratic function.

Example 3: Find the max or min value of

Practice: P 248 – 249: 4, 18, 26

Homework: P 241: 1, 5, 7, 17, 19, 29 P 248 – 249: 3, 7, 11, 13, 15, 23, 25, 37,

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