College Algebra, Unit 4, Practice Milestone 4 - With Answers!!
You passed this Practice Milestone.
When you take the actual Milestone, you must score 50% or higher to
pass.
18 questions were answered correctly.
2 questions were answered incorrectly.
1
What is the product of
and
?
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RATIONALE
To multiply these two polynomials, you can
distribute
into each of the terms inside the
parentheses. First, distribute
into
.

CONCEPT
Multiplying Monomials and Binomials
2
Examine the quadratic function
.
What is the graph of this function?
When multiplying these two terms, you will multiply the
coefficients together and evaluate the multiplication of the
x-terms.
Similar to above, when multiplying these two terms, you
will multiply the coefficients together and evaluate the
multiplication of the x-terms.
The final product is the sum of the two distributions.
The coefficients of 7 and 3 multiply to 21. The
times
equals
. Don't forget to include the one factor of
y. Finally, add both parts together.
The coefficients 7 and 2 multiply to 14. Recall that if two
terms with the same base are multiplied, simply add the
exponents, so
times
equals
. Don't forget to
include the
. Next, distribute
into
.

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RATIONALE
When given a quadratic equation, one way
to determine the graph is by finding the
vertex. Since the equation is in standard
form
, we can identify the
coefficients a and b to put in the vertex
formula.

Once we have substituted a and b, we can
solve for x. First , we will evaluate the
numerator, -(-1), and the denominator, 2(1).
0.5 squared, or (0.5)(0.5), equal 0.25.
Next, solve by subtracting the remaining
values.
0.25 minus 0.5 minus 6 equals -6.25. This
is the value of the y-coordinate of the
vertex.
The vertex is located at (0.5,-6.25). We can
look for the graph that has a vertex at this
point.
A negative -1 is the same as positive 1. 2
times 1 equals 2. The value of the x-
coordinate of the vertex is
, or 0.5. Next,
use this value for x and solve for y in the
original equation,
.
We can substitute in 0.5 for x in the original
equation. To solve for y, first evaluate the
exponent,
.
In the equation
, a is equal to
1 and b is equal to -1. To find the vertex,
use these values for a and b to calculate
the x-coordinate of the vertex by plugging
into the formula
.

CONCEPT
Graphing Parabolas
3
Look at the quadratic equation
.
Find the solutions by using the quadratic formula.
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RATIONALE
This graph, with a vertex of
(0.5,-6.25) corresponds to the quadratic
function
.