AnswersAlgebra III AQuadratic Functions: Standard Form

Introduction to the Quadratic Formula Answers

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Which shows the correct substitution of the values a, b, and c from the equation 0 = – 3x2 – 2x + 6 into the quadratic formula?Quadratic formula: x =

Question illustration
A
x = StartFraction negative (negative 2) plus or minus StartRoot (negative 2) squared minus 4 (negative 3)(6) EndRoot Over 2(negative 3) EndFraction
Option A
B
x = StartFraction negative 2 plus or minus StartRoot 2 squared minus 4 (negative 3)(6) EndRoot Over 2(negative 3) EndFraction
Option B
C
x = StartFraction negative (negative 2) plus or minus StartRoot (negative 2) squared minus 4 (3)(6) EndRoot Over 2(3) EndFraction
Option C
D
x = StartFraction negative 2 plus or minus StartRoot 2 squared minus 4 (3)(6) EndRoot Over 2(3) EndFraction
Option D
2
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What are the values of a, b, and c in the quadratic equation 0 = x2 – 3x – 2?

Question illustration
A
a = , b = 3, c = 2
Option A
B
a = , b = –3, c = –2
Option B
C
a = , b = 3, c = –2
Option C
D
a = , b = –3, c = 2
Option D
3

What is the value of the discriminant, b2 − 4ac, for the quadratic equation 0 = x2 − 4x + 5, and what does it mean about the number of real solutions the equation has?

A
The discriminant is −4, so the equation has 2 real solutions.
B
The discriminant is −4, so the equation has no real solutions.
C
The discriminant is 35, so the equation has 2 real solutions.
D
The discriminant is 35, so the equation has no real solutions.
4

Which statement is true about the quadratic equation 8x2 − 5x + 3 = 0?

A
The constant term is 8.
B
The constant term is −5.
C
The leading coefficient is 8.
D
The leading coefficient is −5.
5

What is the value of the discriminant for the quadratic equation –3 = –x2 + 2x?Discriminant = b2 – 4ac

A
–8
B
4
C
8
D
16
6

A student is deriving the quadratic formula. Her first two steps are shown.Step 1: –c = ax2 + bxStep 2:

Question illustration
A
division property of equality
B
factoring the binomial
C
completing the square
D
subtraction property of equality
7

What is the value of the discriminant for the quadratic equation 0 = x + 2 + x2?Discriminant = b2 – 4ac

A
–9
B
–7
C
7
D
9
8

The first step for deriving the quadratic formula from the quadratic equation, 0 = ax2 + bx + c, is shown.Step 1: –c = ax2 + bx

A
subtraction property of equality
B
completing the square
C
factoring out the constant
D
zero property of multiplication
9

Which shows the correct substitution of the values a, b, and c from the equation 1 = –2x + 3x2 + 1 into the quadratic formula?Quadratic formula:

Question illustration
A
x = StartFraction negative (negative 2) plus or minus StartRoot (negative 2) squared minus 4 (3)(0) EndRoot Over 2(3) EndFraction
Option A
B
x = StartFraction negative (negative 2) plus or minus StartRoot (negative 2) squared minus 4 (3)(2) EndRoot Over 2(3) EndFraction
Option B
C
x = StartFraction negative (negative 2) plus or minus StartRoot (negative 2) squared minus 4 (3)(1) EndRoot Over 2(3) EndFraction
Option C
D
x = StartFraction negative 3 plus or minus StartRoot 3 squared minus 4 (negative 2)(0) EndRoot Over 2(negative 2) EndFraction
Option D
10

Some of the steps in the derivation of the quadratic formula are shown.Step 4: Step 5: Step 6: Step 7:

Question illustration
A
Negative values, like −4ac, do not have a square root.
B
The ± symbol prevents the square root from being evaluated.
C
The square root of terms separated by addition and subtraction cannot be calculated individually.
D
The entire term b2 − 4ac must be divided by 2a before its square root can be determined.

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