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 𝑦=12π‘₯βˆ’4π‘₯?

  • A(1,7)
  • Bο€Ό12,1
  • C(βˆ’1,16)
  • Dο€Όβˆ’12,5
  • E(0,0)

Q2:

Given the graph, evaluate 𝑔(βˆ’1).

Q3:

The function 𝑓(π‘₯)=8π‘₯βˆ’π‘ and the function 𝑔(π‘₯)=2π‘₯βˆ’π‘οŠ¨. Find 𝑓(βˆ’5)+𝑔(βˆ’10) given 𝑓(βˆ’10)+𝑔(βˆ’6)=βˆ’14.

Q4:

Which of the following points is on the graph of the equation π‘₯βˆ’π‘¦=8?

  • A(βˆ’3,1)
  • B(1,3)
  • C(1,βˆ’3)
  • D(βˆ’1,βˆ’3)

Q5:

Find the values of 𝑏 and 𝑐 given the function 𝑓(π‘₯)=βˆ’π‘₯+𝑏π‘₯+π‘οŠ¨, and 𝑓(π‘₯)=βˆ’8 when π‘₯∈{3,βˆ’5}.

  • A𝑏=3, 𝑐=2
  • B𝑏=βˆ’2, 𝑐=7
  • C𝑏=βˆ’5, 𝑐=3
  • D𝑏=βˆ’32, 𝑐=βˆ’5

Q6:

Find the value of 𝑐 given the function 𝑓(π‘₯)=π‘₯+π‘οŠ¨ passes through the point (7,8).

Q7:

Find β„Ž(βˆ’10) given β„Ž(π‘₯)=π‘Žπ‘₯+𝑏π‘₯+π‘οŠ¨ where β„Ž(βˆ’5)=βˆ’35 and {0,2} is the set of zeros for β„Ž(π‘₯).

Q8:

Which of the following is equivalent to 𝑓2√6+1 for the function 𝑓(π‘₯)=π‘₯βˆ’2π‘₯βˆ’3?

  • A10𝑓1βˆ’2√6
  • Bβˆ’10𝑓1βˆ’βˆš6
  • C𝑓1βˆ’βˆš6
  • D10𝑓1βˆ’βˆš6

Q9:

A study of 10,000 people was carried out to investigate the rate of infection of influenza. The number of infections, 𝑦, occurring 𝑛 years after 2004 can be found using the equation 𝑦=βˆ’2.5π‘›βˆ’7.5𝑛+909. 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 β„Ž(𝑑) in feet after 𝑑 seconds have elapsed such that β„Ž(𝑑)=600βˆ’16π‘‘οŠ¨. Express 𝑑 as a function of height β„Ž, and then calculate the time taken to drop to a height of 400 feet to one decimal place.

  • A𝑑=√600βˆ’β„Ž16, 0.88 seconds
  • B𝑑=600βˆ’β„Ž16, 12.5 seconds
  • C𝑑=ο„ž600βˆ’β„Ž16, 3.5 seconds
  • D𝑑=ο„ž600+β„Ž16, 7.9 seconds
  • E𝑑=√600+β„Ž16, 2 seconds

Q11:

The height in feet, 𝑦, of a golf ball can be found using the equation 𝑦=βˆ’16.1𝑑+137𝑑+3, where 𝑑 is the time in seconds after it was struck. Will the ball reach a height of 301 feet?

  • Ayes
  • Bno

Q12:

Consider the function 𝑓(π‘₯)=π‘₯βˆ’10π‘₯+1οŠͺ.

By considering 𝑓 as a quadratic in π‘₯ and using the quadratic formula, find all the values of π‘₯ for which 𝑓(π‘₯)=0.

  • Aπ‘₯=5+2√6, π‘₯=βˆ’ο„5+2√6, π‘₯=5βˆ’2√6, π‘₯=βˆ’ο„5βˆ’2√6
  • Bπ‘₯=5+2√6, π‘₯=5βˆ’2√6
  • Cπ‘₯=5+√15, π‘₯=5βˆ’βˆš15
  • Dπ‘₯=5+√15, π‘₯=βˆ’ο„5+√15, π‘₯=5βˆ’2√15, π‘₯=βˆ’ο„5βˆ’βˆš15
  • Eπ‘₯=5+√34, π‘₯=βˆ’ο„5+√34, π‘₯=5βˆ’2√34, π‘₯=βˆ’ο„5βˆ’βˆš34

Evaluate π‘“ο€»βˆš3+√2 and π‘“ο€»βˆš3βˆ’βˆš2.

  • Aπ‘“ο€»βˆš3+√2=βˆ’24, π‘“ο€»βˆš3βˆ’βˆš2=βˆ’8
  • Bπ‘“ο€»βˆš3+√2=βˆ’36, π‘“ο€»βˆš3βˆ’βˆš2=βˆ’4
  • Cπ‘“ο€»βˆš3+√2=0, π‘“ο€»βˆš3βˆ’βˆš2=0
  • Dπ‘“ο€»βˆš3+√2=36, π‘“ο€»βˆš3βˆ’βˆš2=4
  • Eπ‘“ο€»βˆš3+√2=24, π‘“ο€»βˆš3βˆ’βˆš2=8

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

  • AThe values found using the quadratic formula are not actually zeros of 𝑓(π‘₯).
  • BThe quadratic formula does not give all the zeros of 𝑓(π‘₯).
  • CTwo of the zeros obtained by the quadratic formula can be expressed in terms of √3 and √2.

By using the fact that √3+√2>√3βˆ’βˆš2>0, write 5βˆ’2√6 in terms of √2 and √3.

  • A√3√2
  • Bβˆ’βˆš3βˆ’βˆš2
  • C√3+√2
  • D√3βˆ’βˆš2
  • E√2βˆ’βˆš3

Q13:

Using the quadratic formula, list all the roots of the equation β„Ž(𝑑)=βˆ’14𝑑+3𝑑+1. If necessary, round your answers to 3 decimal places.

  • A𝑑=0,3
  • B𝑑=βˆ’1.325,3.325
  • C𝑑=0.325,βˆ’12.325
  • D𝑑=βˆ’0.325,12.325

Q14:

Using the quadratic formula, list all the roots of the equation 𝑓(π‘₯)=βˆ’4π‘₯+40π‘₯+20. Round your answers to 3 decimal places.

  • Aπ‘₯=βˆ’0.477
  • Bπ‘₯=10.477
  • Cπ‘₯=βˆ’0.477,10.477
  • Dπ‘₯=0.477,βˆ’10.477

Q15:

The height of a ball 𝑑 seconds after it was kicked from the ground is modeled by the function β„Ž, where β„Ž(𝑑)=15π‘‘βˆ’5π‘‘οŠ¨.

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, 𝑦, can be found using 𝑦=βˆ’0.5π‘›βˆ’5.5𝑛+931, where 𝑛 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, 𝑦, occurring 𝑛 years after the start of the study, can be found using the equation 𝑦=βˆ’2.5π‘›βˆ’7.5𝑛+942. What was the value of 𝑛 when there were 347 people infected?

  • A𝑛=17
  • B𝑛=βˆ’17
  • C𝑛=βˆ’14
  • D𝑛=14

Q18:

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

It’s height after launch can be found using 𝑠=343π‘‘βˆ’4.9𝑑, where 𝑠 is the rocket’s height in meters and 𝑑 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 2β€Žβ€‰β€Ž690.1 m above the ground?

  • AThe height after 6 seconds will be 2β€Žβ€‰β€Ž028.6 m. It will be 2β€Žβ€‰β€Ž690.1 m above the ground at 9 s and 61 s.
  • BThe height after 6 seconds will be 2β€Žβ€‰β€Ž234.4 m. It will be 2β€Žβ€‰β€Ž690.1 m above the ground at 10 s and 62 s.
  • CThe height after 6 seconds will be 1β€Žβ€‰β€Ž881.6 m. It will be 2β€Žβ€‰β€Ž690.1 m above the ground at 10 s and 62 s.
  • DThe height after 6 seconds will be 2β€Žβ€‰β€Ž234.4 m. It will be 2β€Žβ€‰β€Ž690.1 m above the ground at 9 s and 61 s.
  • EThe height after 6 seconds will be 1β€Žβ€‰β€Ž881.6 m. It will be 2β€Žβ€‰β€Ž690.1 m above the ground at 9 s and 61 s.

Q19:

A formula for the normal systolic blood pressure for a man age 𝐴, measured in millimeters mercury, is given as 𝑃=0.006π΄βˆ’0.02𝐴+120. 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 𝑑=5𝑑+16π‘‘οŠ¨ ft, where 𝑑 is measured in seconds. How long will it take for the object to travel 74 ft?

Q21:

The equation 𝑍=π‘›βˆ’7.7𝑛+219 can be used to find the population of a country where 𝑍 is the population in millions, and 𝑛 is the number of years after the last census. After how many years will the population be 242 million?

Q22:

Given a production level π‘₯, the cost function of a company is 𝐢=60π‘₯+300, and the revenue function is 𝑅=100π‘₯βˆ’0.5π‘₯. Knowing that profit is equal to revenue minus the cost, find two values of π‘₯ 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, 𝑃, who contracted the flu 𝑑 days after it broke out is given by the model 𝑃=βˆ’π‘‘+13𝑑+130, where 1≀𝑑≀6. Find the day on which 160 students has the flu.

Q24:

Let π‘₯ 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 𝑦."

  • A𝑦=3π‘₯+π‘₯+6
  • B𝑦=π‘₯+π‘₯+6
  • C𝑦=π‘₯+6π‘₯+3
  • D𝑦=6π‘₯+π‘₯+3
  • E𝑦=π‘₯+3π‘₯+6

Q25:

Write an equation that describes the statement β€œThe value of 𝑦 is equal to 4 less than the square of π‘₯.”

  • A𝑦=π‘₯+4
  • B𝑦=(π‘₯+4)
  • C𝑦=4βˆ’π‘₯
  • D𝑦=(π‘₯βˆ’4)
  • E𝑦=π‘₯βˆ’4

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