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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.1What is the product ofand?••••RATIONALETo multiply these two polynomials, you can distributeinto each of the terms inside the parentheses. First, distribute into .
CONCEPTMultiplying Monomials and Binomials2Examine 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 timesequals. 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, sotimesequals. Don't forget to include the . Next, distribute into .
•RATIONALEWhen 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.
CONCEPTGraphing Parabolas3Look at the quadratic equation.Find the solutions by using the quadratic formula.••••RATIONALEThis 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.