# The has been added to to create a perfect square

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The has been added to to create a perfect square trinomial,. However, this is the same as adding , or because ofthe factor in front of the trinomial. We actually needed to add tothe left side to keep it balanced. Next, simplify the left side.The left side can simplify fromto just . On the rightside, we now have a perfect square trinomial. Write this as a binomialsquared.29can be expressed as . Lastly, subtract from bothsides to isolate on the left.This is the equivalent equation written in vertex form.Converting a Quadratic Equation into Vertex Form 16John is driving at a constant speed of 40 miles per hour. An hour and 15 minutesAn hour and 48 minutesAn hour and 30 minutes
An hour and 8 minutesTo find how long it will take John to travel miles, we can use thedistance, rate, time formula and solve for time. Plug in miles forthe distance, and miles per hour for the rate, or speed.Once we have plugged in the values, we need to write miles per houras a fraction: miles over hour.When dividing by a fraction, we can change this into a multiplicationproblem and multiply by the reciprocal of miles perhour, whichwould be hour over miles.Rewrite miles as a fraction over , and multiply this by thereciprocal of mph. Next, multiply the numerators anddenominators of the fractions.Multiplying across the numerator and denominator, produces over . The units of miles cancel, so we are left with hours. Finally, divide by .It will take John hours. However, because we must express ouranswer in hours and minutes, we must convert hours to minutes.Using the conversion factor, minutes to hour, evaluate thefractions by multiplying the numerators and denominators.Multiplying across the numerator and denominator produces times , or . Units of hours cancel, leaving only minutes.It will take John 1 hour and 15 minutes to travel 50 miles at a constantspeed of 40 miles per hour.Distance, Rate, and Time 17
This is the correct answer. The product of two negative numbers is always apositive number. Negative times negative equals positive This is incorrect. The product of a positive and negative number is alwaysnegative. The correct product is This is incorrect. The quotient of a positive and negative number is alwaysnegative. The correct quotient is This is incorrect. The quotient of two negative numbers is always positive. Thecorrect quotient is 5525short dash 12short dash 8
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.Multiplying and Dividing Positive and Negative Numbers 18
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First, apply the Power of a Power Property of Exponents, which states that when anexponent is raised to another exponent, you can multiply the exponents. Therefore,multiply and to evaluate the first part,is equivalent to. Next, combine the two terms. The Product Property ofExponents states that if two expressions with the same base are multiplied together, youcan add the exponents. Add the exponents and to evaluate the two terms.plus is , which becomes the final exponent.Properties of Exponents 19The graph of a linear function passes through the points and
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