Deck 11: Quadratic Equations

Question 1

Draw the graph of the equation and label the vertex. $y = 2 x ^ { 2 } - 10 x + 3$

A)
B)
C)
D)

Answer 1

Question 2

Draw the graph of the equation and label the vertex. $y = - x ^ { 2 } + 2 x + 12$

A)
B)
C)
D)

Answer 2

Question 3

Draw the graph of the equation and label the vertex. $y = \frac { 1 } { 3 } x ^ { 2 } - \frac { 2 } { 3 } x + 8$

A)
B)
C)
D)

Answer 3

Question 4

Draw the graph of the equation and label the vertex. $y = - 3 x ^ { 2 }$

A)
B)
C)
D)

Question 5

Draw the graph of the equation and label the vertex. $y = - \frac { 1 } { 5 } x ^ { 2 }$

A)
B)
C)
D)

Question 6

Draw the graph of the equation and label the vertex. $y = 3 x ^ { 2 } - 6 x - 13$

A)
B)
C)
D)

Question 7

Draw the graph of the equation and label the vertex. $y = 3 ( x - 2 ) ^ { 2 }$

A)
B)
C)
D)

Question 8

Draw the graph of the equation and label the vertex. $y = x ^ { 2 } - 2$

A)
B)
C)
D)

Question 9

Draw the graph of the equation and label the vertex. $y = x ^ { 2 } - 2 x + 1$

A)
B)
C)
D)

Question 10

Draw the graph of the equation and label the vertex. $y = - 3 ( x + 4 ) ^ { 2 }$

A)
B)
C)
D)

Question 11

Draw the graph of the equation and label the vertex. $y = - 0.4 x ^ { 2 } + 2.4 x + 0.7$

A)
B)
C)
D)

Question 12

Draw the graph of the equation and label the vertex. $y = - x ^ { 2 } - 2 x$

A)
B)
C)
D)

Question 13

Draw the graph of the equation and label the vertex. $y = - 2 x ^ { 2 } - 10 x + 10$

A)
B)
C)
D)

Question 14

Draw the graph of the equation and label the vertex. $y = x ^ { 2 } + 4$

A)
B)
C)
D)

Question 15

Draw the graph of the equation and label the vertex. $y = 2 x ^ { 2 } - 4 x - 3$

A)
B)
C)
D)

Question 16

Draw the graph of the equation and label the vertex. $y = x ^ { 2 } - 3$

A)
B)
C)

Question 17

Draw the graph of the equation and label the vertex. $y = \frac { 1 } { 2 } x ^ { 2 }$

A)
B)
C)
D)

Question 18

Draw the graph of the equation and label the vertex. $y = 2 x ^ { 2 }$

A)
B)
C)
D)

Question 19

Draw the graph of the equation and label the vertex. $y = 2 ( x + 3 ) ^ { 2 } - 3$

A)
B)
C)
D)

Question 20

Draw the graph of the equation and label the vertex. $y = 6 x ^ { 2 } - 3 x - 14$

A)
B)
C)
D)

Question 21

Solve the equation. $2 x ^ { 2 } = 5 x - 2$

A) $x = 2 , \quad x = - \frac { 1 } { 2 }$
B) $x = 2 , \quad x = \frac { 1 } { 2 }$
C) $x = - 2 , \quad x = - \frac { 1 } { 2 }$
D) $x = - 2$
E) $x = - 2 , \quad x = \frac { 1 } { 2 }$

Question 22

Solve the equation. $x ^ { 2 } - 4 x + 3 = 0$

A) $x = + 1$ , $x = - 3$
B) $x = 1$ , $x = 3$
C) $x = - 3$ , $x = - 3$
D) $x = - 1$ , $x = + 3$
E) $x = - 1$ , $x = - 3$

Question 23

Solve the equation. $x ^ { 2 } - 110 = x$

A) $x = 11$ , $x = 10$
B) $x = - 11$ , $x = - 10$
C) $x = - 11$ , $x = 10$
D) $x = 11$ , $x = - 10$
E) $x = 11$

Question 24

Solve the equation. $x ^ { 2 } = 64$

A) $x = - 8 , \quad x = - 8$
B) $x = - 64 , \quad x = 8$
C) $x = - 8 , \quad x = 8$
D) $x = - 64 , \quad x = - 8$
E) $x = - 64 , \quad x = 64$

Question 25

Solve the equation. $10 n ^ { 2 } - 35 n = 0$

A) $n = 0 , \quad n = - \frac { 2 } { 7 }$
B) $n = 0 , \quad n = \frac { 2 } { 7 }$
C) $n = 0 , \quad n = - \frac { 7 } { 2 }$
D) $n = 0$
E) $n = 0 , \quad n = \frac { 7 } { 2 }$

Question 26

Solve the equation. $33 x ^ { 2 } + 130 x + 33 = 0$

A) $x = \frac { 11 } { 3 }$
B) $x = - \frac { 11 } { 3 } , x = - \frac { 3 } { 11 }$
C) $x = \frac { 11 } { 3 } , x = - \frac { 3 } { 11 }$
D) $x = \frac { 11 } { 3 } , x = \frac { 3 } { 11 }$
E) $x = - \frac { 11 } { 3 } , x = \frac { 3 } { 11 }$

Question 27

Solve the equation. $w ^ { 2 } + 19 w + 90 = 0$

A) $w = - 9$ , $w = - 10$
B) $w = 9$ , $w = 10$
C) $w = - 9$ , $w = 10$
D) $w = 9$ , $w = - 10$
E) $w = - 9$

Question 28

Solve the equation. $x ^ { 2 } - 13 x = 36$

A) $x = 9$
B) $x = 4$ , $x = 9$
C) $x = 9$ , $x = - 4$
D) $x = - 9$ , $x = - 4$
E) $x = - 9$ , $x = 4$

Question 29

Solve the equation. $6 x ^ { 2 } + 48 x = 0$

A) $x = 0$ , $x = 8$
B) $x = 2$ , $x = 8$
C) $x = 8$
D) $x = 0$ , $x = - 8$
E) $x = 0$

Question 30

Solve the equation. $x ^ { 2 } - x = 42$

A) $x = 6$ , $x = 7$
B) $x = - 6$ , $x = 7$
C) $x = - 6$ , $x = - 7$
D) $x = - 6$ , $x = - 6$
E) $x = - 6$

Question 31

Solve the equation. $9 m = m ^ { 2 }$

A) $m = 9$ , $m = - 9$
B) $m = 0$
C) $m = 0$ , $m = 9$
D) $m = 9$
E) $m = 0$ , $m = - 9$

Question 32

Solve the equation. $9 x = x ^ { 2 }$

A) $x = 9 , \quad x = 9$
B) $x = 0 , \quad x = - 9$
C) $x = 9$
D) $x = 0 , \quad x = 9$
E) $x = 0$

Question 33

A rectangle is 3 ft longer than it is wide. The area of the rectangle is 54 ft ². Use a quadratic equation to find the dimensions of the rectangle.

A) 3 ft, 6 ft
B) 5.5 ft, 9.5 ft
C) 6 ft, 9 ft
D) 8 ft, 11 ft
E) 5 ft, 10 ft

Question 34

Solve the equation. $w ^ { 2 } - 4 w = 0$

A) $w = 0$
B) $w = - 4$ , $w = 4$
C) $w = 0$ , $w = 4$
D) $w = 0$ , $w = - 4$
E) $w = 4$

Question 35

Solve the equation. $x ^ { 2 } - 13 x + 42 = 0$

A) $x = - 6$ , $x = 7$
B) $x = - 6$ , $x = - 7$
C) $x = 6$ , $x = - 7$
D) $x = - 6$ , $x = - 6$
E) $x = 7$ , $x = - 7$

Question 36

Solve the equation. $4 x ^ { 2 } = 25$

A) $x = - \frac { 5 } { 2 } , x = \frac { 2 } { 5 }$
B) $x = - \frac { 2 } { 5 } , x = \frac { 5 } { 2 }$
C) $x = - \frac { 5 } { 2 } , x = \frac { 5 } { 2 }$
D) $x = - \frac { 5 } { 2 }$
E) $x = - \frac { 2 } { 5 } , x = \frac { 2 } { 5 }$

Question 37

Solve the equation. $c ^ { 2 } + 56 = 15 c$

A) $c = - 7$ , $c = - 8$
B) $c = 7$ , $C = 8$
C) $c = 7$ , $c = - 8$
D) $c = 7$
E) $c = - 7$ , $C = 8$

Question 38

Solve the equation. $n ^ { 2 } - 5 n - 24 = 0$

A) $n = 3$ , $n = 8$
B) $n = 3$ , $n = - 8$
C) $n = - 3$
D) $n = - 3$ , $n = 8$
E) $n = - 3$ , $n = - 8$

Question 39

Solve the equation. $c ^ { 2 } - 4 c = 12$

A) $C = 2$
B) $c = - 2$ , $C = 6$
C) $C = 2$ , $c = - 6$
D) $c = - 2$ , $c = - 6$
E) $C = 2$ , $C = 6$

Question 40

Solve the equation. $25 x ^ { 2 } = 81$

A) $x = - \frac { 9 } { 10 } , \quad x = \frac { 9 } { 10 }$
B) $x = - \frac { 9 } { 5 } , x = \frac { 9 } { 5 }$
C) $x = - \frac { 9 } { 5 } , x = \frac { 5 } { 9 }$
D) $x = - \frac { 5 } { 9 } , x = \frac { 9 } { 5 }$
E) $x = - \frac { 5 } { 9 } , x = \frac { 5 } { 9 }$

Question 41

Solve the equation. $x ^ { 2 } + x - 56 = 0$

Question 42

Express the number in terms of j (if necessary, round the result to three significant digits). $\sqrt { - 81 }$

A) 9
B) 81j
C) 9j
D) -9j
E) -9

Question 43

Express the number in terms of j (if necessary, round the result to three significant digits). $\sqrt { - 6 }$

A) $- 2.45 j$
B) $6 j$
C) $2.45$
D) $2.45 j$
E) $- 2.45$

Question 44

Solve the equation. $c ^ { 2 } + 20 = 9 c$

Question 45

Simplify. $j ^ { 46 }$

A) $- j ^ { 3 }$
B) $- j$
C) $1$
D) $- 1$
E) $j$

Question 46

Solve the equation. $x ^ { 2 } - 13 x = - 40$

Question 47

Solve the equation. $x ^ { 2 } - x = 12$

Question 48

Simplify. $j ^ { 35 }$

A) -1
B) $- j$
C) $- j ^ { 3 }$
D) $j$
E) $1$

Question 49

Express the number in terms of j (if necessary, round the result to three significant digits). $\sqrt { - 34 }$

A) $34$
B) $34$ j
C) $5.83$
D) $5.83 j$
E) - $5.83$ j

Question 50

Solve the equation. $x ^ { 2 } - 5 x + 4 = 0$

Question 51

Solve the equation. $2 x ^ { 2 } = 15 x - 7$

Question 52

Express the number in terms of j (if necessary, round the result to three significant digits). $\sqrt { - 5 }$

A) $- 2.24 j$
B) $2.24$
C) $2.24 j$
D) $- 5$
E) $5 j$

Question 53

A rectangle is 7 ft longer than it is wide. The area of the rectangle is 98 ft ². Use a quadratic equation to find the dimensions of the rectangle. length = __________ ft
width = __________ ft

Question 54

Simplify. $j ^ { 14 }$

A) $- j$
B) $j$
C) $j ^ { 3 }$
D) $- 1$
E) $1$

Question 55

Simplify. $j ^ { 17 }$

A) -1
B) - j
C) j
D) j³
E) 1

Question 56

Solve the equation. $77 x ^ { 2 } + 170 x + 77 = 0$

Question 57

Solve the equation. $n ^ { 2 } - 81 = 0$

Question 58

Express the number in terms of j (if necessary, round the result to three significant digits). $\sqrt { - 529 }$

A) $529$ j
B) $23$
C) - $23$
D) - $23$ j
E) $23$ j

Question 59

Simplify. $\frac { 1 } { j ^ { 18 } }$

A) $\frac { 1 } { j ^ { 9 } }$
B) 1
C) -1
D) $j$
E) - $j$

Question 60

Solve the equation. $25 n ^ { 2 } = 49$

Question 61

Simplify.

Question 62

Determine the nature of the roots of the quadratic equation without solving it. $3 x ^ { 2 } + 8 = x$

A) two rational roots
B) one rational root
C) two irrational roots
D) two imaginary roots

Question 63

Solve the quadratic equation using the quadratic formula (if necessary, round the result to three significant digits). $2 x ^ { 2 } = 4 x - 6$

A) $x = 4.5 , x = 3.5$
B) $x = 1 + 4 j , \quad x = 1 - 4 j$
C) $x = 2 + 4 j , \quad x = 2 - 4 j$
D) $x = 2 + 4 j , \quad x = 1 - 4 j$
E) $x = 2 + 1.66 j , \quad x = 2 - 1.66 j$

Question 64

Determine the nature of the roots of the quadratic equation without solving it. $4 x ^ { 2 } - 7 x + 3 = 0$

A) two irrational roots
B) one rational root
C) two rational roots
D) two imaginary roots

Question 65

Simplify.

Question 66

Simplify.

Question 67

Express the number in terms of j (if necessary, round the result to three significant digits).          j

Question 68

Express the number in terms of j (if necessary, round the result to three significant digits). ___

Question 69

Determine the nature of the roots of the quadratic equation without solving it. $8 x ^ { 2 } - 7 x + 3 = 0$

A) two irrational roots
B) one rational root
C) two rational roots
D) two imaginary roots

Question 70

Solve the quadratic equation using the quadratic formula (if necessary, round the result to three significant digits). 2x ² + 1 = x

A) x = 0.250 + 0.661j, x = 0.250 - 0.661j
B) x = 0.250 + 0.707j, x = 0.250 - 0.707j
C) x = 0.125 + 0.707j, x = 0.125 - 0.707j
D) x = 0.125 + 0.661j, x = 0.125 - 0.661j

Question 71

Express the number in terms of j (if necessary, round the result to three significant digits). ____

Question 72

Determine the nature of the roots of the quadratic equation without solving it. __________ root(s)

Question 73

Determine the nature of the roots of the quadratic equation without solving it. $8 x - 1 = 5 x ^ { 2 }$

A) two imaginary roots
B) one rational root
C) two irrational roots
D) two rational roots

Question 74

Solve the quadratic equation using the quadratic formula (if necessary, round the result to three significant digits). $4 x ^ { 2 } + x + 9 = 0$

A) $x = 1.62 , \quad x = 1.62$
B) $x = - 0.063 + 1.50 j , \quad x = - 0.063 - 1.50 j$
C) $x = - 0.125 + 1.50 j , \quad x = - 0.125 - 1.50 j$
D) $x = - 0.063 + 1.49 j , \quad x = - 0.063 - 1.49 j$
E) $x = - 0.125 + 1.49 j , \quad x = - 0.125 - 1.49 j$

Question 75

Determine the nature of the roots of the quadratic equation without solving it. $x ^ { 2 } + 5 = x$

A) two imaginary roots
B) two rational roots
C) one rational root
D) two irrational roots

Question 76

Express the number in terms of j (if necessary, round the result to three significant digits). ____ j

Question 77

Solve the quadratic equation using the quadratic formula (if necessary, round the result to three significant digits). $x ^ { 2 } - x + 3 = 0$

A) $x = 0.5 + 1.58 j , \quad x = 1 - 1.58 j$
B) $x = 0.5 + 1.58 j , \quad x = 0.5 - 1.58 j$
C) $x = 0.5 + 1.66 j , \quad x = 0.5 - 1.66 j$
D) $x = 5 + 1.58 j , \quad x = 5 - 1.58 j$
E) $x = 0.1 + 1.58 j , \quad x = 1 - 1.58 j$

Question 78

Simplify. $j ^ { 23 }$

Question 79

Solve the quadratic equation using the quadratic formula (if necessary, round the result to three significant digits). $x ^ { 2 } + 16 x + 100 = 0$

A) $x = - 8 + 7 j , \quad x = - 8 - 7 j$
B) $x = - 7 + 6 j , \quad x = - 7 - 6 j$
C) $x = - 8 , \quad x = - 8$
D) $x = - 8 + 6 j , \quad x = - 8 - 6 j$
E) $x = - 7 + 7 j , \quad x = - 7 - 7 j$

Question 80

Simplify.