AnswersFL-1200710-Mathematics for College Algebra ASolving Quadratic Equations: Quadratic Formula

Solving Quadratic Equations: Quadratic Formula — Unit test Answers

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Zacharias is using the quadratic formula to solve the equation 0 = –2x2 + 5x – 3. He begins by substituting as shown.Quadratic formula: x = Substitution:

Question illustration
A
The –5 should be 5.
B
The 52 should be –52.
C
The 2 in the numerator should be –2.
D
The 2 in the denominator should be –2.
2
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What are the solutions to x2 + 8x + 7 = 0?

A
x = –8 and x = –7
B
x = –7 and x = –1
C
x = 1 and x = 7
D
x = 7 and x = 8
3

Brianna is graphing the function f(x) = x2 + 6x + 5. What x-intercepts should Brianna use to graph f(x)?

A
–5 and –1
B
–5 and 1
C
–1 and 5
D
1 and 5
4

The sum of a number and its square is 42. Which equation can be used to find the two numbers for which this is true?

A
x2 + x = 42
B
x2 + 2x = 42
C
x2 + x + 42 = 0
D
x2 + 2x + 42 = 0
5

Ramiya is using the quadratic formula to solve a quadratic equation. Her equation is x = after substituting the values of a, b, and c into the formula. Which is Ramiya’s quadratic equation?Quadratic formula: x =

Question illustration
A
0 = x2 + 3x + 2
B
0 = x2 – 3x + 2
C
0 = 2x2 + 3x + 1
D
0 = 2x2 – 3x + 1
6

A group of students is given a 10 by 10 grid to cut into individual unit squares. The challenge is to create two squares using all of the unit squares. Their teacher states that after the two new squares are formed, one should have a side length two units greater than the other.

A
x2 + (x – 2)2 = 10
B
x2 + 2x2 = 10
C
x2 + (x – 2)2 = 100
D
x2 + 2x2 = 100
7

Alessandro wrote the quadratic equation in standard form. What is the value of c in his new equation?

Question illustration
A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
8

Which shows the correct substitution of the values a, b, and c from the equation –2 = –x + x2 – 4 into the quadratic formula?Quadratic formula: x =

Question illustration
A
x = StartFraction negative (negative 1) plus or minus StartRoot (negative 1) squared minus 4 (1)(negative 4) EndRoot Over 2(1) EndFraction
Option A
B
x = StartFraction negative 1 plus or minus StartRoot 1 squared minus 4 (negative 1)(negative 4) EndRoot Over 2(negative 1) EndFraction
Option B
C
x = StartFraction negative (negative 1) plus or minus StartRoot (negative 1) squared minus 4 (1)(negative 4) EndRoot Over 2(1) EndFraction
Option C
D
x = StartFraction negative (negative 1) plus or minus StartRoot (negative 1) squared minus 4 (1)(negative 2) EndRoot Over 2(1) EndFraction
Option D
9

A function g(x) has x-intercepts at (, 0) and (6, 0). Which could be g(x)?

Question illustration
A
g(x) = 2(x + 1)(x + 6)
B
g(x) = (x – 6)(2x – 1)
C
g(x) = 2(x – 2)(x – 6)
D
g(x) = (x + 6)(x + 2)
10

A rectangle has an area of 40 square units. The length is 6 units greater than the width.

A
8 by 5
B
10 by 4
C
11 by 9
D
13 by 7
11

What is the solution to 2x2+8x=x2-16?

A
x=-4
B
x=-2
C
x=2
D
x=4
12

Rounded to the nearest hundredth, what is the positive solution to the quadratic equation 0=2x2+3x-8?Quadratic formula: x =

Question illustration
A
1.39
B
2.00
C
2.89
D
3.50
13

What are the zeros of the function f(x) = x2 + 5x + 5 written in simplest radical form?Quadratic formula: x =

Question illustration
A
x =
Option A
B
x =
Option B
C
x =
Option C
D
x =
Option D
14

What are the values of a, b, and c in the quadratic equation 0 = 5x – 4x2 – 2?

A
a = 5, b = 4, c = 2
B
a = 5, b = –4, c = –2
C
a = –4, b = 5, c = –2
D
a = 4, b = –5, c = –2
15

Which shows the correct substitution of the values a, b, and c from the equation 0 = 4x2 + 2x – 1 into the quadratic formula below?Quadratic formula: x =

Question illustration
A
x = StartFraction negative 2 plus or minus StartRoot 2 squared minus 4(4)(negative 1) EndRoot Over 2(4) EndFraction
Option A
B
x = StartFraction negative 2 plus or minus StartRoot 2 squared minus 4(4)(1) EndRoot Over 2(4) EndFraction
Option B
C
x = StartFraction negative 2 plus or minus StartRoot 2 squared + 4(4)(negative 1) EndRoot Over 2(4) EndFraction
Option C
D
x = StartFraction negative 2 plus or minus StartRoot negative 2 squared minus 4(4)(negative 1) EndRoot Over 2(4) EndFraction
Option D
16

Which equations are true for x = –2 and x = 2? Select two optionsx2 – 4 = 0x2 = –4 3x2 + 12 = 04x2 = 162(x – 2)2 = 0

A
x2 – 4 = 0
B
x2 = –4
C
3x2 + 12 = 0
D
4x2 = 16
E
2(x – 2)2 = 0
17

A quadratic equation of the form 0=ax2+bx+c has a discriminant value of -16. How many real number solutions does the equation have?

A
-1
B
0
C
1
D
2
18

The only solution of the equation x2 + bx + 16 = 0 is x = 4. What is the value of b?

A
b = –16
B
b = –8
C
b = 8
D
b = 16
19

What is the positive solution to the equation 0 = –x2 + 2x + 1?Quadratic formula: x =

Question illustration
A
–2 +
Option A
B
2 –
Option B
C
1 +
Option C
D
–1 +
Option D
20

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

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