CMR/TRIG MIDTERM REVIEW
Linear Regression
1.)
Use your graphing calculator to graph a scatterplot of the
data. Describe the correlation of the data.
2.)
What type of model do you is best based on your plot?
3.)
Find the linear regression model using your calculator.
4.)
What is the best interpretation for the slope of the least
squares regression line?
5.)
What is the best interpretation of the y-intercept of the
least squares regression line.
6.)
Use the linear regression equation to predict the life
expectancy of a person that was born in the year 1955.
7.)
Use the linear regression equation to predict the birth year of
a person who lives to be 97.
8.)
What is the residual for the birth year 1990?
CMR/TRIG MIDTERM REVIEW
Quadratic Functions
GRAPH:
f (x) = −4x 2 + 4x + 8
Steps for graphing quadratic equations:
Find the vertex
Find x-values equidistant from the x-coordinate of the vertex.
vertex
x
f(x)
Follow Up Questions:
Is the quadratic equation in standard form ? _________
a=____ b=____ c=_____
Why does this function graph a parabola ? _____________
What is the axis of symmetry ? __________________
What is the y-intercept ?
__________________
How can you find the y-intercept algebraically?
_____________________________
_____________________________
What are the x-intercepts?
How can you find the x-intercepts algebraically ?
_______________________
_______________________________________
_______________________________________
CMR/TRIG MIDTERM REVIEW
Application of Quadratic Equations
1.) Big Bertha, a cannon used in WWI, could fire shells incredibly long
distances. The path of a shell could be modeled by y = −.0196x 2 + 1.37x ,
where x was the horizontal distance (in miles) and y represents the
height (in miles). How far could Big Bertha fire a shell?
2.) A volcano in Hawaii erupted in 1959 shooting lave hundreds of feet in
the air modeled by h = −16t 2 + 350t where h is the height of the lava
above the ground (in feet) at time t after the eruption began. Find
the maximum height reached by the lava.
3.) The path of an arrow is modeled by h = −16t 2 + 64t + 4 where h is the
height (in feet) of the arrow above the ground t seconds after the
arrow was shot. How long was the arrow in the air?
Quadratic Regression
CMR/TRIG MIDTERM REVIEW
f (x) = (x − 5)2 + 6
x
f(x)
f (x) = −3(x − 2)2 − 2
x
f(x)
Translation of
f ( x) = x 2
Standard Form:
Translation of
Standard Form:
Absolute Value Functions
y=
y = −5 x + 1 + 1
x
y
Shape of Graph ________
Vertex _____________
Opens ______________
Parent Function _________
Translation of Parent Function:
_________________________
Slope: ___________________
f ( x) = x 2
1
x− 3 + 4
2
x
y
Shape of Graph ________
Vertex _____________
Opens ______________
Parent Function _________
Translation of Parent Function:
_________________________
Slope: ___________________
CMR/TRIG MIDTERM REVIEW
Square Root Functions
Plot
y=
x
x+2+5
Plot y =
Domain:
Range:
x
y
How does this shift
Plot y =
y= x
?
− x−3−4
Domain:
Range:
x
y
How does this shift
Plot y =
y= x
?
3 x −1 −1
Domain:
Range:
x
y
How does this shift
Plot y = −
y= x
?
1
x − 3 +1
2
Domain:
Range:
x
y
How does this shift
y= x
?
CMR/TRIG MIDTERM REVIEW
Compostion of Functions and Inverse Functions
h(x) = x2 + 1
f(x) = -x + 5
g(x) = 2x + 4
SOLVE.
f(-3) =
f(h(2))=
f(f(0))=
g(f(x))=
h(f(x))=
f(f(x))=
Find the inverse of the function y = −4 x − 3
Graph y = −4 x − 3 and its inverse .
Then graph the line y = x
to be sure that the graphs reflect
about this line.
Verify that the above functions are inverses.
f(g(x)) = x
AND
g(f(x)) = x
CMR/TRIG MIDTERM REVIEW
Cubic Functions
y = 2x 3 − x 2 − 3x + 1
x
y
Parent Function: __________
a=______
b =______ c =______
d=____
y-intercept: ________
x-intercepts:________
________
________
Local Maximum: ____________
Local Minimum: ____________
End Behavior:
As x → ∞, y → ______
As x → −∞, y → ______
Applications of Cubic Functions
You are designing a box to be made of a piece of cardboard that is 19 inches by 17 inches. The box will be formed by making the square cuts shown in the diagram below. x x x
x
x
x
x
x
x
1.) Provide the formula for the volume of the box in terms of x.
2.) Find the value of x that maximizes the volume of the box.
Rational Functions
CMR/TRIG MIDTERM REVIEW
y=
1
+2
x −1
x
y
Vertical Asymptote:
Horizontal Asymptote:
Domain:
Range:
y=
4x − 3
2x + 2
x
y
Vertical Asymptote:
Horizontal Asymptote:
Domain:
Range: