Quadratics
Math with Dhruv Singla
Key features of Quadratic Relations (vertex, AOS, zeros, optimal value)
The graph of a quadratic relation is called parabola. A parabola has some key important features.
Axis of Symmetry: A vertical line that divides the parabola in half
Vertex: The highest or lowest point of a parabola
Zeros: The point at which the parabola intersects the x-axis
Optimal value: The maxim or minimum value
Quadratic Relations and finite differences
Finite differences determine if the relation is Linier. Quadratic or Neither.
Transformations of Quadratics Y=a(x-h)+k
Y=a(x-h)+k is the equation to a parabola.
A: If positive parabola opening up, if negative parabola opening down
H: The X-intercept of the vertex. If negative parabola will move to the left, If positive the Parabola will move to the right
K: The Y-intercept of the vertex
Finding X and Y intercepts
To find X intercept you must sub 0 In for Y
To find Y intercept you must sub 0 in for X
Example: X=3y+4
X=4(0)+4
X=4
0=3y+4
-4=4y
-1=y
word problems
Multiplying Binomials and Special Products
Example 1: (x+3)^2=(x+3)(x+3) Example 2: (x+3)(x-3)=x^2-3x+3x-9
=x^2+3x+3x+9 =x^2-9
=x^2+6x+9
Factoring simple trinomials
>Ex1: 5y-30 >Ex2: 2x^3-6x
> 5 is the only thing common in this equation >2x is common in this equation
> divide the equation by 5 >divide the equation by 2x
>5(y-6) >2x(x^2-3)
Factoring complex trinomials
Ex1: 4x^4-6x^3+2x^2+2x
>The whole equation divides by 2x
>2x(2x^3-3x^2+x+1)