College Algebra, Unit 4, Practice Milestone 4 - With Answers!!.pdf - College Algebra Unit 4 Practice Milestone 4 With Answers You passed this Practice

# College Algebra, Unit 4, Practice Milestone 4 - With Answers!!.pdf

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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 ? 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 .
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. RATIONALE This graph, with a vertex of (0.5,-6.25) corresponds to the quadratic function .
4 squared equals 16, and 4 times 3 times -15 equals -180. Next, find the difference between 16 and -180. 16 minus -180 is equivalent to 16 plus 180, or 196. Next, take the square root of 196. The square root of 196 is 14. Next, evaluate the denominator by multiplying 2 and 3. 2 times 3 equals 6. To find the solutions, create two equations (due to the ±). When we have a quadratic equation, we can find the solutions by using the quadratic formula.