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".

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

One teacher's answer to "Why Quadratics?"
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