# Worksheet: Evaluating Quadratic Functions

In this worksheet, we will practice evaluating quadratic functions.

**Q1: **

Which of the following is NOT a point on the curve ?

- A
- B
- C
- D
- E

**Q4: **

Which of the following points is on the graph of the equation ?

- A
- B
- C
- D

**Q5: **

Find the values of and given the function , and when .

- A,
- B,
- C,
- D,

**Q7: **

Find given where and is the set of zeros for .

**Q8: **

Which of the following is equivalent to for the function ?

- A
- B
- C
- D

**Q9: **

A study of 10,000 people was carried out to investigate the rate of infection of influenza. The number of infections, , occurring years after 2004 can be found using the equation Calculate the number of infections in 2010 and 2012.

- A884 persons, 839 persons
- B884 persons, 884 persons
- C774 persons, 689 persons
- D900 persons, 913 persons

**Q10: **

An object is dropped from a height of 600 feet. It has a height in feet after seconds have elapsed such that . Express as a function of height , and then calculate the time taken to drop to a height of 400 feet to one decimal place.

- A, 0.88 seconds
- B, 12.5 seconds
- C, 3.5 seconds
- D, 7.9 seconds
- E, 2 seconds

**Q12: **

Consider the function .

By considering as a quadratic in and using the quadratic formula, find all the values of for which .

- A, , ,
- B,
- C,
- D, , ,
- E, , ,

Evaluate and .

- A,
- B,
- C,
- D,
- E,

What can you conclude from the previous two parts of the question?

- AThe values found using the quadratic formula are not actually zeros of .
- BThe quadratic formula does not give all the zeros of .
- CTwo of the zeros obtained by the quadratic formula can be expressed in terms of and .

By using the fact that , write in terms of and .

- A
- B
- C
- D
- E

**Q15: **

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?

**Q16: **

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?

**Q17: **

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?

- A
- B
- C
- D

**Q18: **

A rocket will be launched vertically upwards with a speed of 343 m/s.

Itβs height after launch can be found using where is the rocketβs height in meters and is the time after launch in seconds.

What will be the height of the rocket 6 seconds after launch?

At what times will the rocket be 2βββ690.1 m above the ground?

- AThe height after 6 seconds will be 2βββ028.6 m. It will be 2βββ690.1 m above the ground at 9 s and 61 s.
- BThe height after 6 seconds will be 2βββ234.4 m. It will be 2βββ690.1 m above the ground at 10 s and 62 s.
- CThe height after 6 seconds will be 1βββ881.6 m. It will be 2βββ690.1 m above the ground at 10 s and 62 s.
- DThe height after 6 seconds will be 2βββ234.4 m. It will be 2βββ690.1 m above the ground at 9 s and 61 s.
- EThe height after 6 seconds will be 1βββ881.6 m. It will be 2βββ690.1 m above the ground at 9 s and 61 s.

**Q21: **

The equation can be used to find the population of a country where is the population in millions, and is the number of years after the last census. After how many years will the population be 242 million?

**Q24: **

Let represent an unknown number.

Write an equation that describes the statement "When three times an unknown number is added to the square of the number and 6 is added to the result, the answer is equal to ."

- A
- B
- C
- D
- E

**Q25: **

Write an equation that describes the statement βThe value of is equal to 4 less than the square of .β

- A
- B
- C
- D
- E