# Learning About Quadratics

### Fun With Quadratics!

## REFLECTION

In quadratics 1, I learned about owrabola's, how to read them and how to plot them. Finding all the points to the parabola (vertex, axis of symmetry, x and y intercepts) took a lot of steps but once I got the hang of it, it got easier. The most easiest thing I learned was what it meant when a parabola opened upwards compared to downwards.

Quadratics 2 was slightly easier now that I sort of got the hang of quadratics 1. I learned about quadratics relations and equations like vertex form, standard form and factored form.

Finally, in quadratics 3 I was taught how to solve quadratic equations in all 3 different forms.

Quadratics is a tough unit to fully learn but once I got the hang of each chapter, I understood it more than before.

## What is quadratics?

## EQUATIONS

Standard form: y=ax2+bx+c

Factored form: y=a(x-r)(x-s)

## What is a Parabola?

## STANDARD FORM

a < 0 opens down

a > 0 opens up

a and b will give you the axis of symmetry, also known as the line that is parallel to the parabola.

To find the axis of symmetry use this equation:

x= - b/2a

X intercepts are also called "zero's".

Optimal value simply means the lowest of highest point in a parabola, for example, where ever the U shape touches (whether we're looking for the lowest or highest point) that would be the optimal value.

Completing the square:

You take the square root of not one, but BOTH sides...

(X-4)2= 5

X- 4 = +/- square root(5)

X=4 +/- square root(5)

X=4- square root (5) and x= 4 + square root (5)

Example from: purplemath.com

## VERTEX FORM

A.O.S:

- the h value of vertex

-divides the parabola in half

OPTIMAL VALUE:

-the k value of vertex equation

Ex: y= -(x+7)3+4

A.O.S= 7

Optimal value= 4

## FACTORED FORM

To find axis of symmetry:

Add the 2 x intercepts together and divide by 2

= x value for your vertex

To find y value:

Sub in x and solve for y in the original equation order.

## FACTORING

-Simple trinomial

-Complex trinomial

-Perfect square

-difference of square

COMMON FACTORING:

Write an expression using numbers that can multiply to make that expression

Ex: 3x+6 is 3 (x+2)

SIMPLE TRINOMIAL:

Make coefficient for "a" = 1.

You should choose two numbers that can multiply to the c value and add up to the b value.

COMPLEX TRINOMIAL:

To factor complex trinomials, you should use the method "Guess and Check".

Ex: 3x2 + 13x + 12 factores into ( x + 3) (3x + 4)

CHECK:

(X+3) (3x+4)

=3x2 + 4x + 9 x + 12

=3x2 + 13x + 12

CHECK!

DIFFERANCE OF SQUARES:

what is it?

When the middle term cancels out and has same values but different signs.

Ex: x4 - 7 is x4 + x0 - 7

REMEMBER: a trinomial is a difference of square if it looks like a2 - b2 = (a +b) (a -b)