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Worksheet: Vertex of a Parabola

Q1:

Find the coordinates of the vertex of the function 𝑓 ( π‘₯ ) = βˆ’ 5 + 7 π‘₯ βˆ’ π‘₯ 2 .

  • A ο€Ό βˆ’ 3 1 2 , 7 1 4 
  • B ( 0 , βˆ’ 5 )
  • C ( 7 , βˆ’ 5 4 )
  • D ο€Ό 3 1 2 , 7 1 4 

Q2:

An object is projected such that it follows a parabolic path given by 𝑦 = βˆ’ 0 . 5 π‘₯ + 8 0 π‘₯ 2 , where π‘₯ is the horizontal distance traveled in feet and 𝑦 is the height. Determine how far along the horizontal the object traveled to reach the maximum height.

Q3:

Find the maximum or minimum value of the function , given .

  • AThe minimum value is 0.
  • BThe maximum value is 10.
  • CThe maximum value is 0.
  • DThe minimum value is 10.

Q4:

Find the maximum or minimum value of the function , given .

  • AThe minimum value is 3.
  • BThe maximum value is 6.
  • CThe maximum value is 3.
  • DThe minimum value is 6.
  • EThe minimum value is 15.

Q5:

Find the maximum or minimum value of the function , given .

  • AThe minimum value is 1.
  • BThe maximum value is .
  • CThe maximum value is 1.
  • DThe minimum value is .

Q6:

Find the maximum or minimum value of the function , given .

  • AThe minimum value is 0.
  • BThe maximum value is .
  • CThe maximum value is 0.
  • DThe minimum value is .
  • EThe minimum value is 1.

Q7:

Find the maximum or minimum value of the function , given .

  • AThe minimum value is 2.
  • BThe maximum value is .
  • CThe maximum value is 2.
  • DThe minimum value is .
  • EThe minimum value is 3.

Q8:

Which of these functions has the greatest maximum value?

  • A 𝑓 ( π‘₯ ) = ( π‘₯ + 5 ) βˆ’ ( 2 π‘₯ + 1 1 ) 2 2
  • B 𝑓 ( π‘₯ ) = 7 βˆ’ ( π‘₯ βˆ’ 1 0 ) 2
  • C 𝑓 ( π‘₯ ) = 1 4 π‘₯ βˆ’ 3 π‘₯ 2
  • D 𝑓 ( π‘₯ ) = 6 βˆ’ 5 π‘₯ βˆ’ π‘₯ 2

Q9:

At which value of π‘₯ does the function 𝑓 ( π‘₯ ) = ( π‘₯ + 3 ) + 4 2 have its minimum?

Q10:

A quadratic function has roots of 3 and 5 and a maximum value of 6. What is its vertex form?

  • A 6 ( π‘₯ + 4 ) βˆ’ 6 2
  • B ( βˆ’ 6 ) ( π‘₯ + 4 ) + 6 2
  • C ( π‘₯ + 5 ) βˆ’ 6 2
  • D ( βˆ’ 6 ) ( π‘₯ βˆ’ 4 ) + 6 2
  • E ( π‘₯ βˆ’ 5 ) βˆ’ 6 2

Q11:

The graph 𝑦 = 𝑓 ( π‘₯ ) of a quadratic function is above the π‘₯ -axis when π‘₯ is between 7 and 19 and reaches a maximum of 14. What is 𝑓 ( π‘₯ ) in vertex form?

  • A 𝑓 ( π‘₯ ) = βˆ’ ( π‘₯ βˆ’ 1 3 ) + 1 4 2
  • B 𝑓 ( π‘₯ ) = 7 1 8 ( π‘₯ βˆ’ 1 3 ) + 1 4 2
  • C 𝑓 ( π‘₯ ) = ( π‘₯ βˆ’ 1 3 ) + 1 4 2
  • D 𝑓 ( π‘₯ ) = βˆ’ 7 1 8 ( π‘₯ βˆ’ 1 3 ) + 1 4 2
  • E 𝑓 ( π‘₯ ) = βˆ’ 7 1 8 ( π‘₯ βˆ’ 1 3 ) βˆ’ 1 4 2