# Quadratics

### MPM2D0-A

## Table Of Contents

**Vertex Form**

- Vertex Form Equation
- Axis of Symmetry, Optimal Value
- Solving for (a) Value
- Zeroes
- Graphing Vertex Form

**Factored Form**

- Expanding and Simplifying Binomials
- Simple Trinomial Factoring
- Complex Trinomial Factoring
- Common Factoring
- Factoring by Grouping
- Perfect Square
- Difference of Sqaures

## WHAT IS A QUADRATIC ?

## Vertex Form

The written equation for vertex form is y=a(x-h)²+k.

The (a) value of the equation determines if the parabola is a vertical stretch or compressed. If the (a) value is less than one, the parabola will be compressed. If the (a) value is one or greater than the parabola is vertically stretched. The (-h) value and (k) value of the equation are the vertex coordinates of the parabola. The vertex is the highest point in the parabola. The (-h) value is the x coordinate the (k) value is the y coordinate. The vertex also gives the axis of symmetry and optimal value.

## Axis of Symmetry/ Optimal Value

## Solving for ''a'' Value

## Transformation

**Vertical Stretch or Compressed?**

The (a) value either makes the parabola stretch vertically or compress.

If the (a) value is less than one it compresses, if its one or more it vertically stretches.

**Direction of Opening**

The direction of opening is the term used to say whether the parabola is opening up or down.

The parabola will have a direction of opening facing up if the (a) value is positive.

If the (a) value is negative the parabola will have a direction of opening facing down. There is a reflection on the x axis when the (a) value is negative.

## Graphing Vertex Form

Example; y=(x+4)^2

## Factored Form

## Graphing Factored Form

The (a) value still multiplies the step pattern or reflects the parabola, just like how it did in vertex form. In vertex form we are give the vertex in the equation, well in factored form we are given the two x intercepts. The (r) and (s) values are the x intercepts of the parabola. One thing to remember is, if the (r) or (s) value is negative. When we graph the parabola the x intercept will not be negative it will be positive. If the (r) or (s) value is positive then the x intercepts will be negative.

For Example : (x-4)(x+2)

Notice how the x-ints are switched.