In the proof of the quadratic formula, the missing reason for the statement "x squared plus b over a times x plus the quantity b over 2 times a squared equals negative 4 times a times c all over 4 times a squared plus b squared over 4 a squared" is:
- Square the right side of the equation
A portion of the quadratic formula proof is shown. Fill in the missing statement.
Statements Reasons
x squared plus b over a times x plus the quantity b over 2 times a squared equals negative 4 times a times c all over 4 times a squared plus b squared over 4 a squared Find a common denominator on the right side of the equation
x squared plus b over a times x plus the quantity b over 2 times a squared equals b squared minus 4 times a times c all over 4 times a squared Add the fractions together on the right side of the equation
the quantity x plus b over 2 times a squared equals b squared minus 4 times a times c all over 4 times a squared Rewrite the perfect square trinomial on the left side of the equation as a binomial squared
x plus b over 2 times a equals plus or minus the square root of b squared minus 4 times a times c, all over 4 times a squared Take the square root of both sides of the equation
x plus b over 2 times a equals plus or minus the square root of b squared minus 4 times a times c, all over 2 times a Simplify the right side of the equation
? Subtract the quantity b over 2 times a from both sides of the equation
x equals b plus or minus the square root of b squared minus 4 times a times c, all over 2 times a
x equals negative b plus or minus the square root of b squared minus 4 times a times c, all over a
x equals negative b plus or minus the square root of b squared minus 4 times a times c, all over 2 times a
x plus b over 2 times a equals negative b plus or minus the square root of b squared minus 4 times a times c, all over 2 times a
Question 6(Multiple Choice Worth 1 points)
(08.03 MC)
A portion of the quadratic formula proof is shown. Fill in the missing reason.
Statements Reasons
ax2 + bx + c = 0 Given
ax2 + bx = −c Subtract c from both sides of the equation
x squared plus b over a times x equals negative c over a Divide both sides of the equation by a
x squared plus b over a times x plus the quantity b over 2 times a squared equals negative c over a plus the quantity b over 2 times a squared Complete the square and add the quantity b over 2 times a squared to both sides
x squared plus b over a times x plus the quantity b over 2 times a squared equals negative c over a plus b squared over 4 times a squared Square the quantity b over 2 times a on the right side of the equation
x squared plus b over a times x plus the quantity b over 2 times a squared equals negative 4 times a times c over 4 times a squared plus b squared over 4 times a squared ?
Find a common denominator on the right side of the equation
Square the right side of the equation
Take the square root of the right side of the equation
Multiply the right side of the equation by a
Question 7(Multiple Choice Worth 1 points)
(08.03 MC)
Solve for x using the quadratic formula: x2 + 2x + 1 = 0
x equals negative b plus or minus the square root of b squared minus 4 times a times c, all over 2 times a
x = 2
x = 1
x = 0
x = −1
Question 8(Multiple Choice Worth 1 points)
(08.03 MC)
When the solution of x2 − 9x − 6 is expressed as 9 plus or minus the square root of r, all over 2, what is the value of r?
x equals negative b plus or minus the square root of b squared minus 4 times a times c, all over 2 times a
6
42
57
105
Question 9(Multiple Choice Worth 1 points)
(08.03 MC)
Use the quadratic formula, x equals negative b plus or minus the square root of b squared minus 4 times a times c, all over 2 times a, to solve the equation 2x2 + 10x − 6 = 0. Round to the nearest hundredths place.
x = −5.54 and x = 0.54
x = −0.54 and x = 5.54
x = −4.30 and x = −0.70
x = −22.17 and x = 2.17
Question 10(Multiple Choice Worth 1 points)
(08.03 LC)
Identifying the values a, b, and c is the first step in using the quadratic formula to find solution(s) to a quadratic equation.
What are the values a, b, and c in the following quadratic equation?
−3x2 − 5x + 9 = 0
a = 5, b = 9, c = 0
a = 3, b = 5, c = 9
a = −3, b = −5, c = 9
a = −5, b = 9, c = 0
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FDK201.12
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