why are they called "quadratics?"

from latin "quadrus" which means SQUARE

what is the tough thing about quadratics?

the fact that they are squared.. We have to undo that x^{2}. We want to get it linear!!

How do we handle that squared term? how can we undo it?

by either splitting the x's apart by factoring, or by taking a square root somewhere..

Why is it called a "linear" term

alone its graph would be a straight line

why is it called a constant term

alone it would be a constant function.. The same height always. a horizontal line with a constant y, a constant height

why is it called a discriminant?

because it discriminates between which type of solutions, roots and zeros you will have (2real, one real or imaginary)

Geometrically, how is the shape of a parabola made?

A parabola is the set of all points equidistant from point, called the focus, and a line, called the directrix.

Are all quadratics similar?

YES.. THEY ALL HAVE THE EXACT SAME SHAPE.. They are simply zoom-ins or zoom-outs of eachother..

Why do parabolas look different if they are all similar?

Well.... Simply either imagine zooming way in or zooming way out... this method can always get any 2 parabolas to look the same.

f(x)= 3x^{2}-4x+5 What is a, b and c ?

a = 3, b = -4, c = 5

f(x)= 3x^{2}-6x+3 What is the axis of symmetry?

-b/2a = -(-6)/2(3) = 6/6 = 1

f(x)= 5 - 2x +3x^{2} What is a, b and c ?

a = 3, b = -2, c = 5

f(x)= -4x^{2} + 8 What is a, b and c ?

a = -4, b = 0, c = 8

f(x)= 3x - 9 What is a, b and c?

a = 0 , b = 3, c = 9..

There is no quadratic term.. THIS IS LINEAR!!! IT'S A LINE!

slope of

f(x)= 6x^{2}- 7x What is a, b and c ?

a = 6, b=-7, c = 0

f(x)= 6x^{2}- 5x What is the axis of symmetry?

x= -b/2a = -(-5)/2(6) = 5/12, AOS x= 5/12

f(x)= -4x^{2} + 8 What is the axis of symmetry?

x= -b/2a = -0/2(-4) = 0/8 = 0. AOS is x=0, which is the y axis!!

What are the five ways to solve a quadratic?

set to zero and factor, complete square, quadratic formula, graph and look for x-intercepts, or when there is no linear term, isolate the x^{2 }and root both sides.

When can you just isolate the x^{2} and root both sides?

when there are no linear terms (only quad and const)

How do you know when it is a quadratic?

when the highest degreed term is the x^{2} term (quadrus:square)

f(x)= 3x^{2}-6x+3 What is the quadratic term?

3x^{2}

f(x)= 3x^{2}-6x+3 What is the linear term?

-6x

f(x)= 3x^{2}-6x+3 What is the constant term?

3, it is the also the y intercept

what is a coefficient?

the number in front of a variable or variables

f(x)= 3x^{2}-6x+3 What is the coefficient of the quadratic term?

3 this is also known as "a"

f(x)= 3x^{2}-6x+3 What is the coefficient of the linear term?

-6 this is also known as "b"

f(x)= 3x^{2}-6x+3 What is the coefficient of the constant term?

3 this is also known as "c"

what is the quadratic term's exponent on the x ?

2

what is the linear term's exponent on the x ?

1

what is the constant term's exponent on the x?

0