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# Quadratic Functions Hello

by MathyCathy## — 32628

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This is the "Parent Function" for Quadratics - x can't be zero!

Standard Form for a Quadratic Function: a, b and c are real numbers, and "a" can't be zero - if it were, the "squared term" would disappear... bye bye parabola :-(

Graph this - it's definitely not linear! Quadratic functions make parabolas, not lines.

The "first differences" here are: -3, -1, +1, +3. There is NOT a constant rate of change.

The "first differences" here are constant - each input is 1 more than the previous input, so each difference is "+1".

Look at the "second differences"... notice anything?

Quadratic functions graph parabolas with smooth curves, not lines.

Since "a" is positive 1, this parabola is "Concave Up, Like a Cup" or is "Happy" like a smile.

Since "a" is -1, this parabola is "Concave Down, Like a Frown" or is "sad".

This vertex is a minimum. It is the lowest point of this parabola located at (0, 0)

This vertex is a maximum. It is the highest point on this parabola, located at (1, 2).

D: all real numbers
R: y is greater than or equal to 0

D: all real numbers
R: y is less than or equal to 2

<div>Here, the "Axis of Symmetry" is the vertical line x = 0. It passes through the vertex of the parabola, (0, 0).</div>

<div>Here, the "Axis of Symmetry" is the vertical line x = 1. It passes through the vertex of the parabola, (1, 2).</div>

The x-intercepts are called the "zeros of the function" because y=0 at these points. Sometimes these x-intercepts are also called "roots".

More information than you want to know about quadratic functions!
www.mathsisfun.com

Why Quadratics?
www.mathworksheetscenter.com

One teacher's answer to "Why Quadratics?"
mathmaine.wordpress.com
Exploration of why quadratic equations are worth learning about: how they are related to linear equations and other polynomials, some of the skills students will learn by studying quadratics, and e…

Quadratics and... Angry Birds!
www.huffingtonpost.com

<div>Created by Cathy Yenca</div>
www.mathycathy.com

Explore graphs of parabolas at Desmos.com!
www.desmos.com

www.desmos.com
Graphing Quadratic Functions

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