What is a Quadratic function?
A Quadratic function is a function that
has the form y=ax²+bx+c. When it is
graphed it is a parabola. The parabola
can be upright or upsidedown depending
on the sing of “a”. It can also be wider or
skiner depending on the absolute value
of “a”
Quadratic functions
Linear function
Standard form: Y=ax²+bx+c
Vertex form: y=a(x-h) ²+k
When it is graph it is a parabola
One variable solved for x
When it is graph it is a line
Slope= rise/run
->
y₁-y₂/x₁-x₂
Slope intercept form: y=mx+b
Point slope form: y-y₁ = m (x-x₁)
Linear:
Quadratics:
To graph quadric functions you use : y=a(x-b) ²+c
C:
Moves vertex up or down C units
positive goes up
Negative goes down
Less than 0
B:
Moves vertex left or right B units
Positive – left
Negative - right
A:
More than 0
Less than 0 – Goes down (like a rainbow)
More than 0- Goes up (like a horse shoe).
Greater than 1 – skinier
Less than 1 - wider
When the parabola opens up, it has a
minimum value at the vertex and when it
opens down it has a maximum value at the
vertex.
STEPS:
1. GRAPH THE FUNCTION
•
IDENTIFY A, B AND C
•
CALCULATE BY USING –B/(2 A) BY
PLUGGING IN THE NUMBERS.
•
USE T-TABLE TO GRAPH
2. FIND X-INTERCEPT(S) ON THE GRAPH
3. YOUR SOLUTIONS ARE THE XINTERCEPTS.
1.Leave X² alone
2.Find the square root of the numbers
3.If the one of the numbers or the
number has no exact square root, then
factor the number and find the square
root of one or both of thoes numbers.
4.Then write pluss minus infront the
number.
STEPS:
1.WRITE THE EQUATION IN STANDARD FORM
2.FIND GCF
3.CANCEL GRATEST COMMON FACTOR BY
DIVIDING THAT NUMBER ON BOTH SIDES
4.FACTOR THE TRINOMIAL
5.EQUAL EACH FACTOR TO 0
6.SOLVE EACH LINEAR EQUATION
Steps:
1.The coeficient of X² must be =1
2.Isolate C
3.Complete the square
4.Add (b/2)² to both sides
5.Write as a binomial squared.
6.Solve by using square root both sides
7.Dont forget the +- (pluss minus)
8.Isolate the variable
Steps:
1. Write in standard
form your
equation.
2.Find a, b, c
3.Plug them in the
formula
4.solve
The Quadratic Formula:
To solve a quadratic
eqation we can first
calculate the
discriminant to
determine number of
solutions. If the
discriminant is positive,
the equation has two
solutions. If it is 0 it
has one solution. If it is
negative, then the
equation has no real
solution.