Quadratics and Functions Problems Workshop 3

Question 1

What is the discriminant used for in quadratic equations?

Answer 1

To determine the number of solutions

Question 2

How many solutions does the equation x² + 4x + 1 = 0 have?

Answer 2

2 solutions

Question 3

How many solutions does the equation 3x² + 4x + 2 = 0 have?

Answer 3

no solutions

Question 4

How many solutions does the equation 2x² - 8x + 8 = 0 have?

Answer 4

1 solution

Question 5

What is the value of k for which the equation x² + kx + (k - 1) = 0 has only one solution?

Answer 5

k = 2

Question 6

What is the y-intercept of the function y = x² + 4x + 3?

Answer 6

3

Question 7

What are the x-intercepts of the function y = x² + 4x + 3?

Answer 7

−1, −3

Question 8

What is the turning point of the function y = x² + 4x + 3?

Answer 8

(−2, −1)

Question 9

What is the maximum height of the rocket given by h(t) = −5t² + 30t?

Answer 9

45 m

Question 10

How many seconds after launch will the rocket reach its maximum height?

Answer 10

3 s

Question 11

When will the rocket hit the ground according to h(t) = −5t² + 30t?

Answer 11

6 s

Question 12

What is the domain of the function f(x) = √(x - 5)?

Answer 12

Df = {x ∈ R | x ≥ 5}

Question 13

What is the range of the function f(x) = √(x - 5)?

Answer 13

Rf = {y ∈ R | y ≥ 0}

Question 14

What is f(14) for the function f(x) = √(x - 5)?

Answer 14

3

Question 15

What is f(9) for the function f(x) = √(x - 5)?

Answer 15

2

Question 16

What is f(5) for the function f(x) = √(x - 5)?

Answer 16

0

Question 17

What is f(0) for the function f(x) = √(x - 5)?

Answer 17

undefined

Question 18

What are the domains of the functions 2x - 3y = 6, y = x² - 7x + 12, and f(x) = 1/(x + 1)?

Answer 18

R

Question 19

What are the ranges of the functions 2x - 3y = 6, y = x² - 7x + 12, and f(x) = 1/(x + 1)?

Answer 19

R

Question 20

What is the composition f◦g(x) for f(x) = x² and g(x) = x + 1?

Answer 20

f◦g(x) = (x + 1)²

Question 21

What is the composition g◦f(x) for f(x) = x² and g(x) = x + 1?

Answer 21

g◦f(x) = x² + 1

Question 22

What percentage of yeast would you expect to give an average weight gain of 70 grams, given G = −200P² + 200P + 20?

Answer 22

0.50%

Question 23

What are the x-intercepts of the quadratic equation y = −x² + 4x?

Answer 23

0, 4

Question 24

What is the turning point of the quadratic equation y = −x² + 4x?

Answer 24

(2, 4)

Question 25

What is the domain of the function f(x) = 1/(x - 2)?

Answer 25

Df = {x ∈ R | x ≠ 2}

Question 26

What is the range of the function g(x) = √x?

Answer 26

Rg = {y ∈ R | y ≥ 0}

Question 27

Does the composition h(x) = g(f(x)) have any asymptotes?

Answer 27

yes, x = 2, y = 0