Completing the Square and Solving Quadratic Equations
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Question 2
You transformed the quadratic equation
y=4x2−20x+24y equals 4 x squared minus 20 x plus 24
into its vertex form
y=4(x−2.5)2−1y equals 4 times the quantity x minus 2 and 5 tenths squared minus 1. Fill in the blanks to find the zeros of the quadratic equation. Use decimals or fractions as needed.
Answer:Correct! Go to question 3.Incorrect. The answer is:
y=4(x−2.5)2−1y equals 4 times the quantity x minus 2 and 5 tenths squared minus 1
Set the equation equal to zero (y=0)y equals zero
: 4(x−2.5)2−1=04 times the quantity x minus 2 and 5 tenths squared minus 1 equals zero
Add 1 to both sides of the equation: 4(x−2.5)2=14 times the quantity x minus 2 and 5 tenths squared equals 1
Divide both sides of the equation by 4: (x−2.5)2=14the quantity x minus 2 and 5 tenths squared equals 1 divided by 4
Square root both sides of the equation: √(x−2.5)2=±√14The square root of the quantity x minus 2 and 5 tenths squared equals plus or minus the square root of 1 divided by 4
Simplify: x−2.5=±12x minus 2 and 5 tenths equals plus or minus one half
Solve for x: x=2.5±12x equals 2 and 5 tenths plus or minus one half
[using fraction:
x=52±12]x equals five halves plus or minus one half
x=2
and 3
Go to question 3.
Incorrect. Refer to the ‘Steps for Solving Quadratic Equations in Vertex Form’ to help you, and try again.