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Introduction to the Quadratic Formula Answers

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What are the values of a, b, and c in the quadratic equation –2x2 + 4x – 3 = 0?

A
a = 2, b = 4, c = 3
B
a = 2, b = 4, c = –3
C
a = –2, b = 4, c = 3
D
a = –2, b = 4, c = – 3
2
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Determine the discriminant for the quadratic equation 0=-2x2+3. Based on the discriminant value, how many real number solutions does the equation have?Discriminant = b2-4ac

A
0
B
1
C
2
D
24
3

What is the value of the discriminant for the quadratic equation 0 = 2x2 + x – 3?Discriminant = b2 – 4ac

A
–25
B
–23
C
25
D
26
4

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.
5

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
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

Some of the steps in the derivation of the quadratic formula are shown.Step 3: –c + = aStep 4a: –c + = aStep 4b: + = a

Question illustration
A
factoring a polynomial
B
multiplication property of equality
C
converting to a common denominator
D
addition property of equality
8

Determine the discriminant for the quadratic equation -3=x2+4x+1. Based on the discriminant value, how many real number solutions does the equation have?Discriminant = b2-4ac

A
0
B
1
C
2
D
12
9

Which is the graph of a quadratic equation that has a positive discriminant?

A
On a coordinate plane, a parabola opens up. It goes through (negative 1, 4), has a vertex at (1, 0), and goes through (3, 4).
Option A
B
On a coordinate plane, a parabola opens up. It goes through (negative 3, 4), has a vertex at (negative 1, 0), and goes through (1, 4).
Option B
C
On a coordinate plane, a parabola opens up. It goes through (negative 2, 5), has a vertex at (0, 1), and goes through (2, 5).
Option C
D
On a coordinate plane, a parabola opens up. It goes through (negative 2, 3), has a vertex at (0, negative 1), and goes through (2, 3).
Option D
10

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