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 x2. 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)= 3x2-4x+5 What is a, b and c ?
a = 3, b = -4, c = 5
f(x)= 3x2-6x+3 What is the axis of symmetry?
-b/2a = -(-6)/2(3) = 6/6 = 1
f(x)= 5 - 2x +3x2 What is a, b and c ?
a = 3, b = -2, c = 5
f(x)= -4x2 + 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!
f(x)= 6x2- 7x What is a, b and c ?
a = 6, b=-7, c = 0
f(x)= 6x2- 5x What is the axis of symmetry?
x= -b/2a = -(-5)/2(6) = 5/12, AOS x= 5/12
f(x)= -4x2 + 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 x2 and root both sides.
When can you just isolate the x2 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 x2 term (quadrus:square)
f(x)= 3x2-6x+3 What is the quadratic term?
f(x)= 3x2-6x+3 What is the linear term?
f(x)= 3x2-6x+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)= 3x2-6x+3 What is the coefficient of the quadratic term?
3 this is also known as "a"
f(x)= 3x2-6x+3 What is the coefficient of the linear term?
-6 this is also known as "b"
f(x)= 3x2-6x+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 ?
what is the linear term's exponent on the x ?
what is the constant term's exponent on the x?