Question 1
Solve for x using the Quadratic Formula: x2 − 6x + 9 = 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 = 6
x = 3
x = 1
x = 0
Question 2
Solve: 49x2 − 60 = 0
Round your answer to the nearest hundredth.
x = 0
x = −3.32 and x = 3.32
x = −1.11 and x = 1.11
x = −0.82 and x = 0.82
Question 3
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 4
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?
−6x2 = −9x + 7
a = 9, b = 7, c = 6
a = −9, b = 7, c = −6
a = −6, b = 9, c = −7
a = −6, b = −9, c = 7
Question 5
Use the quadratic formula to find the exact solutions of x2 − 5x − 2 = 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 equals 5 plus or minus the square root of 33, all over 2
x equals negative 5 plus or minus the square root of 33, all over 2
x equals 5 plus or minus the square root of 17, all over 2
x equals negative 5 plus or minus the square root of 17, all over 2
Question 6
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 7
The quadratic equation 3x2 + 45x + 24 = 0 was solved using 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.
One solution is −14.45. What is the other solution? Round to the hundredths place.
−1.11
−0.55
0.52
14.45
Question 8
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, was used to solve the equation. 2x2 − 8x + 7 = 0. Fill in the missing denominator of the solution.
4 plus or minus the square root of 2, all over blank
−16
2
4
14
Question 9
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?
−6x2 − 8x + 12
a = −6, b = −8, c = 12
a = 6, b = 8, c = 12
a = 8, b = 12, c = 0
a = −8, b = 12, c = 0