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

Q2:

Given the graph, evaluate . Q3:

The function and the function . Find given .

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,

Q6:

Find the value of given the function passes through the point .

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

Q11:

The height in feet, , of a golf ball can be found using the equation , where is the time in seconds after it was struck. Will the ball reach a height of 301 feet?

• Ayes
• Bno

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

Q13:

Using the quadratic formula, list all the roots of the equation . If necessary, round your answers to 3 decimal places.

• A
• B
• C
• D

Q14:

Using the quadratic formula, list all the roots of the equation . Round your answers to 3 decimal places.

• A
• B
• C
• D

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.

It’s height after launch can be found using where is the rocket’s 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 2‎ ‎690.1 m above the ground?

• AThe height after 6 seconds will be 2‎ ‎028.6 m. It will be 2‎ ‎690.1 m above the ground at 9 s and 61 s.
• BThe height after 6 seconds will be 2‎ ‎234.4 m. It will be 2‎ ‎690.1 m above the ground at 10 s and 62 s.
• CThe height after 6 seconds will be 1‎ ‎881.6 m. It will be 2‎ ‎690.1 m above the ground at 10 s and 62 s.
• DThe height after 6 seconds will be 2‎ ‎234.4 m. It will be 2‎ ‎690.1 m above the ground at 9 s and 61 s.
• EThe height after 6 seconds will be 1‎ ‎881.6 m. It will be 2‎ ‎690.1 m above the ground at 9 s and 61 s.

Q19:

A formula for the normal systolic blood pressure for a man age , measured in millimeters mercury, is given as . Find the age, to the nearest year, of a man whose normal systolic blood pressure measures 125 mmHg.

Q20:

A falling object travels a distance given by the formula ft, where is measured in seconds. How long will it take for the object to travel 74 ft?

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?

Q22:

Given a production level , the cost function of a company is , and the revenue function is . Knowing that profit is equal to revenue minus the cost, find two values of for which the profit is \$300 by solving a quadratic equation.

• A66, 14
• B72, 8
• C60, 20
• D76, 4
• E30, 10

Q23:

An epidemiological study of the spread of a certain influenza strain that hit a small school population found that the total number of students, , who contracted the flu days after it broke out is given by the model , where . Find the day on which 160 students has the flu.

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 “The value of is equal to 4 less than the square of .

• A
• B
• C
• D
• E