Quadratic relations
By Deepak Gogna
Topics
Transformation of quadratics
Quadratic relations
Graphing y=(h-k)2+k
factored form- Y=a(x-r)(x-s
special product
multiplying polynomials
common factors
factor quadratic expression of form x2+bx+c
factor quadratic expression of form ax2+bx+c
factor a perfect square trinomial and difference of squares
maxima and minima
solve quadratic equations
graph quadratics using the x-intercept
The quadratic formula
solving word problems using the quadratic formula
What is quadratics?
Factored form is : y= a(x-r)(x-s)
Standard Form is : y =ax2 + bx + c
A quadratic relationship is shown by a parabola.
You can tell if its a quadratic by first and second differences.
Transformation of quadratics
Transformations:
The (-h) moves the vertex of the parabola left or right
The (k) moves the vertex of the parabola up or down
The (a) stretches the parabola and if the
Vertex= (h,k)
Once the vertex of a parabola is indicated the step pattern is used to find the rest of the points.
optimal value
complex factoring
The different about complex factoring is that it does not have a coeffiecient of 1 and there are no common factors.
An example is :
4x^2 +6x + 4
common factoring
First take out all common factors in equation
Also take out any common variables
Mission is to take out all common factors
simple factoring
Perfect Squares
A perfect square is a square of a whole number, a number that is squarable.
A perfect square's equation looks like
a^2 + 2ab +b^2
difference of squares
A difference of squares equation looks like...
a^2 - b^2
The quadratic formula
Step 1: Find the coefficients a , b and c
Step 2: Plug in the values for a, b, and c into the quadratic formula
Step 3: Simplify
Step 4: Solve for X
step pattern
Maxima and Minima
Maxima and minima are the lowest or highest
points on a parabola. When the vertex is the lowest point on the parabola
then it is know as the minimum value. Also If the vertex is at the highest point on
the parabola then it is know as the maximum value.
Multiplying polynomials
Connections
When you are changing standard form into vertex form you have to use factoring
Lastly When you are converting vertex form into standard form you have to use expanding and simplifying