Forms of a Quadratic Function
Give the characteristics of a Quadratic Function
Degree of 2; "U-shaped" graph known as a parabola
What is the purpose of using Completing the Square on an equation?
To get an equation from Standard Form into Vertex Form
How many solutions do you get when taking the square root of a number?
TWO; one positive and one negative
Solve:
x2-4x-12
x=-2
x=6
What is the equation of a parabola with a vertex at (1 , -8) and passes through the point (2 , -6)?
y=2(x-1)2-8
What is Standard Form?
f(x)=ax2+bx+c
Put into Vertex Form:
y=x2-6x+2
y=(x-3)2-7
Solve:
x2=25
x=-5
x=5
Solve:
x2 + 14x - 15
x= -15
x= 1
What is Factored Form?
f(x)= a(x-r)(x-s)
Put into Vertex Form:
y=x2-9x+14
y=(x-9/2)2-25/4
Solve:
9x2+25=0
No Solution
*cannot have a negative sign under radical
Solve:
5x2+53x+30
x=-10
x=-3/5
What direction does a parabola point if the leading coefficient is negative?
What is Vertex Form?
f(x)= a(x-h)2+k
Put into Vertex Form:
y=2x2+16x-24
y=2(x+4)2-56
Solve:
(x−6)2−5=0
x=6 - square root of 5
x=6 + square root of 5
Solve:
3x2-7x
x=0
x=7/3
How do you tell if a parabola is increasing or decreasing?
Start by reading the graph from left to right. If the range of the graph is increasing (moving toward positive numbers), the graph is increasing. If the range of the graph is decreasing (moving toward negative numbers), the graph is decreasing. Remember: increasing and decreasing intervals are only expressed by values on the x-axis!
In f(x)=a(x-h)2+k, what is the vertex?
(h,k)
*keep in mind the sign in front of h flips when you take it out of the parentheses*
Solve by Completing the Square:
x2 + 4x - 21 = 0
x= -7, 3
Solve:
(x−10)2−1=0
x=11
When you factor a quadratic, you are really finding the x-intercepts on a parabola. What is another word for x-intercepts?
Zeros
The value of "C" tells us the Y-intercept or Initial Value