# Quadratic Relationships

### By: Bikram Dhaliwal

## What is a Quadratic relation?

A quadratic relation is the involvement of relations of unknown quantity and variables

## 1st difference and 2nd difference

## 1 Transformation

## 2 Transformation

## 3 Transformation

## Word problem using vertex form

## Summary Of The Vertex Form

**What is the purpose of vertex form?**

- Tells you if the parabola is stretched or compressed
- You can find out if it opens up or down
- Tells you the vertex

**What does H value mean?**

- Tells you the x value of the vertex

**What does K value mean?**

- Tells you the y value of the vertex
- If the value is positive the vertex moves up
- If the value is negative the vertex moves down

## Graph

## Vertex Form Word Problem (Video)

## Graphing Using Transformations (Video)

## Sources

"Graphing Quadratic Transformations (Grade 10 Academic Lesson 4.4).mov."*YouTube*. N.p., n.d. Web. 18 Mar. 2016.

"Graphing Quadratic Equations." N.p., n.d. Web.

"Vertex+form - Google Search." *Vertex+form - Google Search*. N.p., n.d. Web. 18 Mar. 2016.

"DIGI 203 Algebra 1 - Graphing a Quadratic Function in Vertex Form." *DIGI 203 Algebra 1 - Graphing a Quadratic Function in Vertex Form*. N.p., n.d. Web. 18 Mar. 2016.

## Learning goals

I learned how to graph vertex form

I learned 1st differences and 2nd differences

## Part #2

## Factored form

The form of an algebraic expression in which no part of the expression can be made simpler by pulling out a common factor.

ex. The factored form of the expression x2+x-2 is (x+2)(x-1).

## Common Factors

When we find all the factors of two or more numbers, and some factors are the same ("common"), then the largest of those common factors is the Greatest Common Factor.

Abbreviated "GCF". Also called "Highest Common Factor"

Example: the GCF of 12 and 16 is 4, because 1, 2 and 4 are common factors of both 12 and 16, and 4 is the greatest.

## Graphing factored form

## Converting factored form to standerd form

## Multiplying Polynomials

- multiply
**each term**in one polynomial by**each term**in the other polynomial - add those answers together, and simplify if needed

## Special Products

(x+2)2=

=(x+2)(x+2) and then just solve it like a regular polynomial

## Factor quadratic expressions of the form x2+bx+c

Here are the steps to factoring a trinomial of the form *x* 2 + *bx* + *c* , with *c* > 0 . We assume that the coefficients are integers, and that we want to factor into binomials with integer coefficients.

- Write out all the pairs of numbers which can be multiplied to produce
*c*. - Add each pair of numbers to find a pair that produce
*b*when added. Call the numbers in this pair*d*and*e*. - If
*b*> 0 , then the factored form of the trinomial is (*x*+*d*)(*x*+*e*) . If*b*< 0 , then the factored form of the trinomial is (*x*-*d*)(*x*-*e*) . - Check: The binomials, when multiplied, should equal the original trinomial.

## Factor Quadratic Expression of the Form ax2+bx+c

## Factoring a perfect square

## Word Problem

## Learning Goals

I learned what special products are.

I learned how to factor a perfect square.

## Part 3

## Chapter 6

## Maxima and Minima

Example: A ball is thrown in the air. Its height at any time t is given by:

h = 3 + 14t − 5t2

What is its maximum height?

h = 0 + 14 − 5(2t)

= 14 − 10t

Now find when the **slope is zero**:

14 − 10t = 0

10t = 14

t = 14 / 10 = **1.4**

The slope is zero at **t = 1.4 seconds**

And the height at that time is:

h = 3 + 14×1.4 − 5×1.42

h = 3 + 19.6 − 9.8 = **12.8**

And so:

The maximum height is **12.8 m** (at t = 1.4 s)

## Completing the square

## Solving Quadratic Equations

## Word Problems Using Quadratic Formula

## More Word Problems

## My Video

## Assesment

## Reflection

## Learning Goals

Solving Quadratic Equations

Maxima and Minima