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Brief Review of Linear and Quadratic Functions
Do all of these without using your calculator. You may use
your calculator to check your
work.
1. Solve the equations for x.
a. 23(52x)+7x = 3x +8
b.
c. 3x^{2}  7x = 6 (Solve by factoring.)
d. 2x^{2} +1= 5x
2. Find the equation of the line that passes through the point (3, 5) and has
slope of
2/3. Write the equation in slope intercept form . Graph this line.
3. Find the slope of the line through the points (325, 126) and (416, 519).
4. Graph the function . What is the xintercept?
5. If xy data is graphed with x representing the number of acres and y
representing
the number of cows , what are the units on the slope of the line between two of
the
data points?
6. Find the x and yintercepts and complete the square to find the vertex .
Graph the
function
f (x) = 2x^{2} + 5x 12.
7. Let
.
a. Find the domain of f.
b. Find f(5).
c. Find f(x2).
d. How does the graph of f(x2) differ from the graph of f(x)?
e. How does the graph of f(x)2 differ from the graph of f(x)?
f. How does the graph of 0.2f(x) differ from the graph of f(x)?
Partial Solutions and Answers .
1.Solve the equations for x.
a. 13x13=3x+8 so x = 21/10 or 2.1.
b. 8x9=10 and so x=19/8 or 2.375.
c. (x3)(3x+2)=0 and so x=3, x= 2/3 are solutions.
d. Using the quadratic formula
2. is the slopeintercept form. Check your graph on the
calculator..
3.
4. The xintercept is 40/3. Check the graph on your calculator.
5.
. Units on slope are the vertical axis units divided by the horizontal
axis units.
6. yintercept (Set x=0): y=12
xintercepts (Set y=0 and solve the quadratic equation ): x = 3/2 and x= 4.
Vertex : note :
vertex :
7. Let .
a. Find the domain of f. Cannot take square roots of negative numbers so x+4 is
greater than 0. Cannot divide by 0 so x+4 does not equal 0. Answer: x> 4.
b.
c.
d. Shift f(x) 2 units to the right.
e. Shift f(x) 2 units down.
f. Graph is vertically shrunk by a factor of 0.2.
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