Quadratic Functions
What is the line called down the middle of the parabola?
The line of symmetry
What is the form of a exponential function?
f(x)=ax
or y=abx
What is a function whose graph forms a straight line called?
A linear function
What is the difference in the shape of a linear and exponential function?
an exponential function can be a parabola and a linear function is a straight line
Find the a, b, c of the following quadratic function:
20x2+ 43x -20 = 0
a = 20
b = 43
c = -20
state the vertex: y=2x2+20x+53
Vertex (-5,3)
In Exponential function what does the "a" stand for? how is it represented on the graph?
initial value the y-intercept
What is the standard form of a linear equation?
y=mx+b
What variable do all three equations have?
x
Simplify the following:
10x(5 + 2x)
50x + 20x2
Factor completely: 4x2-20x+25
(2x-5)2
What does f(x) represent in an exponential function?
dependent variable or output of the function
What are the independent and dependent variables in a linear equation?
Independent variable: x
Dependent variable: y
What are the three functions we are comparing?
Quadratic, exponential, linear
Simplify the following:
10x2 - 5 + 5x2 - 8x + 12
15x2 -8x + 8
Factor completely using two methods: 10x2-35x-20
5(x-4)(2x+1)
Is this equation exponential : y=3x-2
No, this is a linear function
Is this equation linear: x3 +y = -1
No, because x has an exponent other than one.
What makes key features of function graphs different?
The x and y-intercepts, intervals where the function is increasing, decreasing, positive or negative.
9(x - 3) = 10x - 7x(x - 2)
9x2 - 27 = 24x - 7x2
factor the following: y=3x2-x-2
(3x+2)(x-1)
less than 1
What are the steps to solving a linear equation?
1) Simplify each side
2) Use -/+ properties to move the variables to one side
3) Use multiplication/division
4)Check your answer
5) Solve for the variable
What does the x represent in each function?
Quadratic: variable number
Exponential: Constant rate
Linear: Figure number
Find the slope of the following:
y = -4x + 10
m = -4