5.1 modeling data with quadratic functions quadratic function: a function that can be written in the...

5.1 Modeling Data with Quadratic Functions Quadratic function: a function that can be written in the standard form of f(x) = ax 2 + bx + c where a does not equal 0

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5.1 Modeling Data with Quadratic Functions

Quadratic function: a function that can be written in the standard form of

f(x) = ax2 + bx + cwhere

a does not equal 0

cbxaxxf 2)(

Quadratic term Linear term Constant term

quadratic. considered is 2 of degree

aith function wany 0,a Since

Page 3: 5.1 Modeling Data with Quadratic Functions Quadratic function: a function that can be written in the standard form of f(x) = ax 2 + bx + c where a does

Classifying Functions

ex: (2x + 3) (x – 4) ex: 4(x2 + 5) – 2(2x2- 9x)

Determine if the function is linear or quadratic. Identify the quadratic, linear and constant terms.

Page 4: 5.1 Modeling Data with Quadratic Functions Quadratic function: a function that can be written in the standard form of f(x) = ax 2 + bx + c where a does

Parabolas:The graph!!!!

Axis of Symmetry

• The line that divides a parabola into 2 parts that are mirror images.

Vertex

• The point at which the parabola intersects the axis of symmetry.

• Is also known as the maximum or the minimum point on the graph.

Page 5: 5.1 Modeling Data with Quadratic Functions Quadratic function: a function that can be written in the standard form of f(x) = ax 2 + bx + c where a does

Examples of parabolas

Page 6: 5.1 Modeling Data with Quadratic Functions Quadratic function: a function that can be written in the standard form of f(x) = ax 2 + bx + c where a does

Ex: Label the axis of symmetry and the vertex. State if the vertex is a max or a min.

Page 7: 5.1 Modeling Data with Quadratic Functions Quadratic function: a function that can be written in the standard form of f(x) = ax 2 + bx + c where a does

Ex: Label the axis of symmetry and the vertex. State if the vertex is a max or a min.

Page 8: 5.1 Modeling Data with Quadratic Functions Quadratic function: a function that can be written in the standard form of f(x) = ax 2 + bx + c where a does

Homework

10/25: #30 pg 241 1-15

Sketching quadratic functions To sketch a quadratic function we need to identify where possible: The y intercept (0, c) The roots by solving ax 2 + bx

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