Worksheet: Vertex of a Parabola

In this worksheet, we will practice identifying the coordinates of a vertex of a quadratic graphically and algebraically and whether it is a maximum or a minimum.

Q1:

Find the coordinates of the vertex of the function 𝑓 ( 𝑥 ) = 5 + 7 𝑥 𝑥 2 .

  • A 3 1 2 , 7 1 4
  • B ( 0 , 5 )
  • C ( 7 , 5 4 )
  • D 3 1 2 , 7 1 4

Q2:

At which value of 𝑥 does the function 𝑓 ( 𝑥 ) = ( 𝑥 + 3 ) + 4 2 have its minimum?

Q3:

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

  • A 6 ( 𝑥 + 4 ) 6 2
  • B ( 6 ) ( 𝑥 + 4 ) + 6 2
  • C ( 𝑥 + 5 ) 6 2
  • D ( 6 ) ( 𝑥 4 ) + 6 2
  • E ( 𝑥 5 ) 6 2

Q4:

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

  • A 𝑓 ( 𝑥 ) = ( 𝑥 1 3 ) + 1 4 2
  • B 𝑓 ( 𝑥 ) = 7 1 8 ( 𝑥 1 3 ) + 1 4 2
  • C 𝑓 ( 𝑥 ) = ( 𝑥 1 3 ) + 1 4 2
  • D 𝑓 ( 𝑥 ) = 7 1 8 ( 𝑥 1 3 ) + 1 4 2
  • E 𝑓 ( 𝑥 ) = 7 1 8 ( 𝑥 1 3 ) 1 4 2

Q5:

Find the maximum or minimum value of the function 𝑓 ( 𝑥 ) = 𝑥 + 1 0 2 , given 𝑥 [ 3 , 3 ] .

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

Q6:

An object is projected such that it follows a parabolic path given by 𝑦 = 0 . 5 𝑥 + 8 0 𝑥 2 , where 𝑥 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.

Q7:

Which of these functions has the greatest maximum value?

  • A 𝑓 ( 𝑥 ) = ( 𝑥 + 5 ) ( 2 𝑥 + 1 1 ) 2 2
  • B 𝑓 ( 𝑥 ) = 7 ( 𝑥 1 0 ) 2
  • C 𝑓 ( 𝑥 ) = 1 4 𝑥 3 𝑥 2
  • D 𝑓 ( 𝑥 ) = 6 5 𝑥 𝑥 2

Q8:

The vertex of the curve of a quadratic function is a maximum point if the sign of the coefficient of 𝑥 2 is , and is a minimum point if the sign of the coefficient of 𝑥 2 is .

  • A negative, positive
  • B positive, negative

Q9:

Find the maximum or minimum value of the function 𝑓 ( 𝑥 ) = 𝑥 6 𝑥 + 1 5 2 , given 𝑥 [ 0 , 6 ] .

  • 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.

Q10:

Find the maximum or minimum value of the function 𝑓 ( 𝑥 ) = 𝑥 2 𝑥 1 5 2 , given 𝑥 [ 2 , 4 ] .

  • AThe minimum value is 1.
  • BThe maximum value is 1 6 .
  • CThe maximum value is 1.
  • DThe minimum value is 1 6 .

Q11:

Find the maximum or minimum value of the function 𝑓 ( 𝑥 ) = 𝑥 5 2 , given 𝑥 [ 3 , 3 ] .

  • AThe minimum value is 0.
  • BThe maximum value is 5 .
  • CThe maximum value is 0.
  • DThe minimum value is 5 .
  • EThe minimum value is 1.

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