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Worksheet: Applications of Quadratic Equations
Q9:
The sum, , of the first consecutive integers can be found using Starting from 1, how many consecutive integers are required to make a sum of 21?
Q10:
The height of a ball seconds after it was kicked from the ground is modeled by the function , where .
For how long does the ball remain in the air?
For how long does the ball remain above a height of 10 m?
Q11:
Which of the following exceeds its multiplicative inverse by ?
- A or 5
- B or
- C 6 or
- D or
Q12:
A study was carried out to determine how many people in a small town were infected with the hepatitis C virus. An approximation for the number of infected people, , can be found using , where is the number of years after 2006. In which year do we expect there to be no infected people?
Q13:
The length of a rectangle is 26 cm more than its width. Given that its area is 120 cm2, determine its perimeter.
Q14:
The length of a rectangle is 15 cm more than its width. Given that its area is 54 cm2, determine its perimeter.
Q15:
The length of a rectangle is 10 cm more than its width. Given that its area is 24 cm2, determine its perimeter.
Q16:
Find the solution set of the equation in .
- A
- B
- C
- D
- E
Q17:
Given that nine times the square of is 25, what are the possible values of ?
- A
- B or
- C5 or
- D or
Q18:
Determine the positive number whose square exceeds twice its value by 15.
Q19:
Find the positive number whose square is equal to two times the number.
Q20:
The difference between the square of Danielβs age now and 5 times his age 2 years ago is 160. How old is Daniel now?
Q21:
At which values of does the graph of cross the -axis?
- A0 and 2
- B0 and
- C0 and
- D0 and
- E0 and
Q22:
When twice the square of a number is added to 1, the result is 99. What is the number?
- A98
- B10 or
- C10
- D7 or
Q23:
Find two numbers with a sum of 10 and a product of 9.
- A8, 2
- B5, 5
- C3, 7
- D1, 9
- E6, 5
Q24:
A study was carried out to investigate the number of people in a town infected by norovirus. The number of people infected, , occurring years after the start of the study, can be found using the equation What was the value of when there were 347 people infected?
Q25:
The length of a rectangle is 3 cm more than double the width. The area of the rectangle is 27 cm2. Write an equation that can be used to find , the width of the rectangle, in centimeters.
- A
- B
- C
- D
- E