Learning About Quadratics

Fun With Quadratics!

REFLECTION

During the start of quadratics, I was having trouble with understanding the basic steps, quadratics 2 was a little bit more challenging but I knew if I could get the hang of it that quadratics 3 would be a little less difficult for me. After school, I would do homework questions and review the product so I would hopefully get a better understanding, and I thought that I did but my tests showed otherwise. On unit tests, I would usually blank out which was not beneficial for my grades, I needed a new strategy. Quadratics may not be my biggest strength but I sure did learn a lot from this unit, and the unit being broken down into separate chapters made it easier for me to understand.

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?

A QUADratic is a variable that gets squares, Quad is another work for square.
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EQUATIONS

Vertex form: y=a(x-h)2+k


Standard form: y=ax2+bx+c


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

What is a Parabola?

A parabola is a symmetrical, U shaped curve that connects points on a graph. A parabola can either be upwards meaning it's positive or downwards meaning its negative.
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STANDARD FORM

The first number you see (a), shows you if your parabola is negative or positive.

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

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VERTEX FORM

Vertex form is quite similar to standard form, but vertex also gives you the tip of the parabola.


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

Quadratic Equations in Standard Form

FACTORED FORM

In factored form, you are given 2 x intercepts, an optimal value, and axis of symmetry.


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.

Quadratic equation - factored form

FACTORING

-Common

-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)

http://youtu.be/tvnOWloeeaU