2. It is a polynomial function that takes the form:
ax^2+bx+c=0 where a does not equal zero.
The above function ^ is the “standard
form”.
We are trying to solve for “x”
This produces a graph that is a parabola
(will explain later).
What is the Quadratic Function?
4. “a”, “b”, and “c” are all known values which
means they are given to you.
“a” will never equal zero.
“x” is the variable (the one we will try to
figure out).
Breaking Down the Equation
ax^2+bx+c
5. x^2+5x+7=0 is a traditional quadratic
function.
x^2= 3x-1 is a quadratic function! Just move
all of the terms to one side by subtracting 3x-1
from both sides and you will get
x^2-3x+1=0 then you may begin to solve
How to spot a Quadratic Function
6. There are 3 ways to go about solving the
Quadratic
Factoring
Completing the Square
THE QUADRATIC FORMULA (song to follow)
How to solve a Quadratic Function
7. We we break down the function by finding the factors of the
equation (something we multiply by).
Example problem: x2 + 3x – 4
The factors are: (x+4)(x-1).
Why?
Because: (x+4)(x-1) = x(x-1) + 4(x-1)
= x2 - x + 4x – 4
= x2 + 3x - 4 (the original function)
Solving by Factoring
8. Now that we have found the factors, (x+4)(x-1) we set
them both equal to zero by getting “x” by itself.
(x+4)=0, x+4-4=0-4 so x=-4
(x-1)=0, x-1+1=0+1 so x=1
Then plug x=-4 and x=1 back into the original equation (x2 +
3x – 4) to check your answers.
Solving by Factoring Cont.
9. Original Function: x2 + 3x – 4=0
Plug in -4 for x to check
(-4)^2+3(-4)-4=0 this checks out so -4 is an answer.
Plug in 1 for x to check as well
1^2+3(1)-4 this checks out as well
So our answers are 1 and -4
Solving by Factoring Cont.
10. Take the original: ax^2+bx+c and turn it into: a(x-h)^2
+ k = 0
To convert from vertex form to standard form we
have to multiply out the squared term. To covert from
standard form to vertex form we have to complete
the square.
Solving by Completing the Square
11. Original: s(x)=x^2-6x+8
Find the square of half of the coefficient of the x-term
So that would be (-6/2)^2=9
And do: s(x)=x^2-6+9-9+8
Which equals: s(x)=(x-3)^2-1
The vertex of s is (3,-1) and the axis of symmetry is the
vertical line x=3.
Solving by Completing the Square
Example
12. Take the oringinal: ax^2+bx+c=0 into:
Finally Solving by the Quadratic
Formula
