# Learning Grade 10 Quadratics

### Sahra B

## First and Second differences

## Investigating Vertex form

## Graphing Vertex Form & analyzing

You plot the vertex which is (h,k)

And then you follow the steps pattern which is a,3a , 5a and etc.

## Converting Factored form to Standard form

To convert into standard form you expand and simply.

Step 1 - Multiply the binomials

Step 2 - Collect like terms

Step 3 - Distribute 'a' value to result.

## Factoring by grouping & Common factoring

**Polynomial form (4 terms) : ax^3+bx^2+cx+d**

1. Find common factors for ax^3 , bx^2

2. Find common factors for cx+d

3. Put common factor outside of each bracket and put the remainder inside of bracket

4. Now you have to group, two brackets should have same number, and the common factors outside of bracket , group them.

## Finding x-interept by setting y=0

1) Set your Y as 0 and solve for x for each binomial

## Factoring trinomials with leading 1

We want our equation to go from **ax^2+bx+c **to **y=a(x-r)(x-s)**

1) Find any common factors

2) Find a number that multiplies to 'c' (aka last number) & adds to 'bx' (aka middle number)

3) Once those two numbers are chosen make two brackets both with 'x' as first number and the second number the numbers you had chosen.

## Factoring trinomials WITHOUT leading 1

**without**a leading number that is 1 , which means that your first term will not just be 'x^2 ' it will be for eg. '6x^2' .

Our goal is to get it from standard form to factored form.

1) Find a common factor in your equation

2) Find two numbers that multiplies to last number (C)

3) Find two numbers that multiplies to first number (ax)

4) Cross multiply & if doesn't equal your sum then change the numbers around or find new numbers.

5) Group them

## Factoring special trinomials

## Standard form : y=ax^2+bx+c

## Getting your x intercepts from Quadratic formula.

a=2 b=9 c=6

Plug in the numbers in the quadratic formula & solve.

## Axis of Symmetry

In order to find the axis of symmetry for a standard form equation you need to know your 'a' and 'b'.The formula to find axis of symmetry in standard form is -b/2a

Ex.Y=2x^2+8x+5

Our a is 2 and our b is 8.

-8

(2)(2)

A.O.S = -2

## Optimal Value

Finding Optimal Value !

To find the optimal value all you need to do is replace the "x" in the equation with the A.O.S and then solve.

Y=2x^2+8x+5

Y=2(-2)^2+8(-2)+5

Y=2(4)-16+5

Y=8-16+5

Y=-3

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