Homework 6 1. Solve each equation below for the variable. Visualize the bags of coins if you are uncertain about a next step. a. 24 – 6w = 7 + 5w b. z + 3 = 29 – 2z c. 8q + 16 = 15q - 33 2. Find the point of intersection of each pair of equations. Experiment with different methods. Some may seem easier for some problems and not for others. You might want to earn some extra good karma and do a problem in more than one way. a. p = 3r – 8 and 2r + p = 22 b. 3f + 2g = 30 and f + 2g = 26 c. 2b – c = 3 and 6b = 5c -1 3. Here is part of the table of a linear function. Figure out the equation of the function. Explain in words how you found the equation. r s 4 8 6 14 Homework 5 1. Here is a list of equations in factored form and another list in vertex form. ON A SEPARATE SHEET OF PAPER, Write each of the equations in factored form next to the equivalent equation in vertex form. Either show your work to justify each choice or explain your reason for it. y = 2(x+4)(x–6) y=2(x+1)2 – 50 y = (x-2)(x-2) y = (x-2)2 y = (x-7)(x-11) y = (x-9)2 – 4 y = 2(x–4)(x+6) y = 2(x–9)2 –8 y = 2(x–7)(x–11) y = 2(x–1)2 – 50 2. Write the equation for each graph in factored form and in vertex form: The value for ‘a’ in y=a(x-h)2+k, and y=a(x-p)(x-q) is given for each graph. a. a = 1 b. a = -1 (THIS HOMEWORK IS CONTINUED ON THE BACK OF THIS SHEET.) c. a = 3 3. Write each of the equations below in standard form (ie. y = ax2+bx+c): a. y = 3(x–7)(x+4) b. y = 2(x–3)2 + 5 c. y = –2(x+3)(x+5) d. y = –3(x–4)2 + 8 4. Find the area and perimeter of the shape below. Explain your work. Homework 4 1. Write a formula for a function with a graph that has exactly two x- intercepts, one at x = 4 and the other at x = 2. Draw a graph by hand of your equation and check its intercepts by substituting 2 and then 4 for x. 2. Write an equation for a function with a graph that has exactly two x- intercepts, one at x = –6 and the other at x = 3. Draw a graph by hand of your equation and check the intercepts. 3. Write a formula for a function whose graph has exactly three x-intercepts, one at x = –3, another at x = 1, and the third at x = 3. Draw a graph by hand of your equation and check the intercepts. 4. Do you think it’s possible to create a function with any given set of x- intercepts? Explain your answer. 5. Draw a graph of a different parabola that has the same x-intercepts as the graph for problem 1. What is the equation of that function? 6. Solve the equation Q = 4a + 6ac for a. Homework 3 1. Find five pairs of numbers (a,b) which are solutions to ab = 70. (Note that you can use negative numbers and fractions.) 2. Write down five number pairs that are solutions to ab = 95. (Note that you can use negative numbers and fractions.) 3. Write down five number pairs that are solutions to ab = 0. (Note that you ca.

1. Homework 6
1. Solve each equation below for the variable. Visualize the
bags of coins if
you are uncertain about a next step.
a. 24 – 6w = 7 + 5w
b. z + 3 = 29 – 2z
c. 8q + 16 = 15q - 33
2. Find the point of intersection of each pair of equations.
Experiment with
different methods. Some may seem easier for some problems
and not for
others. You might want to earn some extra good karma and do a
problem
in more than one way.
a. p = 3r – 8 and 2r + p = 22
b. 3f + 2g = 30 and f + 2g = 26
c. 2b – c = 3 and 6b = 5c -1
3. Here is part of the table of a linear function. Figure out the
equation of the
function.

2. Explain in words how you found the equation.
r s
4 8
6 14
Homework 5
1. Here is a list of equations in factored form and another list in
vertex form.
ON A SEPARATE SHEET OF PAPER, Write each of the
equations in
factored form next to the equivalent equation in vertex form.
Either show
your work to justify each choice or explain your reason for it.
y = 2(x+4)(x–6) y=2(x+1)2 – 50
y = (x-2)(x-2) y = (x-2)2
y = (x-7)(x-11) y = (x-9)2 – 4
y = 2(x–4)(x+6) y = 2(x–9)2 –8
y = 2(x–7)(x–11) y = 2(x–1)2 – 50
2. Write the equation for each graph in factored form and in
vertex form:
The value for ‘a’ in y=a(x-h)2+k, and y=a(x-p)(x-q) is given for
each graph.
a. a = 1

3. b. a = -1
(THIS HOMEWORK IS CONTINUED ON THE BACK OF THIS
SHEET.)
c. a = 3
3. Write each of the equations below in standard form
(ie. y = ax2+bx+c):
a. y = 3(x–7)(x+4)
b. y = 2(x–3)2 + 5
c. y = –2(x+3)(x+5)
d. y = –3(x–4)2 + 8
4. Find the area and perimeter of the shape below. Explain your
work.

4. Homework 4
1. Write a formula for a function with a graph that has exactly
two x-
intercepts, one at x = 4 and the other at x = 2. Draw a graph by
hand of
your equation and check its intercepts by substituting 2 and then
4 for x.
2. Write an equation for a function with a graph that has exactly
two x-
intercepts, one at x = –6 and the other at x = 3. Draw a graph
by hand of
your equation and check the intercepts.
3. Write a formula for a function whose graph has exactly three
x-intercepts,
one at x = –3, another at x = 1, and the third at x = 3. Draw a
graph by
hand of your equation and check the intercepts.
4. Do you think it’s possible to create a function with any given
set of x-
intercepts? Explain your answer.

5. 5. Draw a graph of a different parabola that has the same x-
intercepts as the
graph for problem 1. What is the equation of that function?
6. Solve the equation Q = 4a + 6ac for a.
Homework 3
1. Find five pairs of numbers (a,b) which are solutions to ab =
70. (Note that
you can use negative numbers and fractions.)
2. Write down five number pairs that are solutions to ab = 95.
(Note that you
can use negative numbers and fractions.)
3. Write down five number pairs that are solutions to ab = 0.
(Note that you can
use negative numbers and fractions.)
4. How is the answer to Question 3 different from the first two?
5. Write five number pairs (g, h) to solve (g – 3)(h + 2) = 95.
(Note that you can
use negative numbers and fractions.)
6. Write five number pairs (g, h) to solve (g – 3)(h+ 2) = 0.

6. (Note that you can
use negative numbers and fractions.)
7. Was Question 5 or Question 6 easier for you? Why?
8. The values in the table below belong to a linear function.
a) What is the slope of the graph of the function?
b) What is the y-intercept?
c) Draw the graph of the function.
d) Write the equation of the function.
e) Make up a situation that fits the function.
x y
3 7
5 13
10 28
Homework 2
1. Write an equivalent expression without parentheses for each
of the
following expressions.

7. a. 3(P + 4)
b. 6(z – 7)
c. 12(y + 3)
2. In the class work, The Why of It, you saw three ways of
thinking about
why 2(X + 1) is equivalent to 2X + 2. Now use those ideas to
explain your
work in Question 1.
a. Use Caroline’s repeated addition method to explain why your
answer to Question 1a is equivalent to 3(P + 4).
b. Use Nickie’s numerical example method to explain why your
answer to Question 1b is equivalent to 6(z – 7).
c. Use Johan’s area model method to explain why your answer
to
Question 1c is equivalent to 12(y + 3).
3. Write an equivalent expression without parentheses for each
of the
following expressions. Use any method you like, but explain
your work
in both cases.
a. (b + 3)(b + 5)
b. (2c + 3)(c + 6)
4. A function has a y-intercept of 3 and its slope is – !
!

8. . Make a table with at
least 3 lines for the function and draw its graph.
Homework 1
A swimmer who weighs 130 pounds using a sidestroke burns
about 472 calories
an hour. A swimmer who weighs 155 pounds using a sidestroke
burns about 563
calories an hour.
1. Use these two data points to draw a graph and a line of best
fit for the
data.
2. Use the graph to approximate how many calories a 190-
pound
swimmer burns using a sidestroke in an hour.
3. Write an equation that fits your graph.
4. Use that equation to calculate the number of calories a 190-
pound
swimmer burns using a sidestroke in an hour.
5. Explain in words how you found the equation in number 3.

9. Review Problem
6. Mangos and Oranges: Maisha went to Berkeley Bowl and
spent
$9.20 on 6 mangos and 5 oranges. Talida stopped at Berkeley
Bowl
on the same day and paid $7.60 for 3 mangos 10 oranges. Show
how
to use equations to figure out the prices for mangos and oranges
that day at Berkeley Bowl.