Lesson: Vertex of a Parabola

In this lesson, we will learn how to identify the coordinates of a vertex of a quadratic graphically and algebraically and whether it is a maximum or a minimum.

Video

10:18

Sample Question Videos

  • 02:07
  • 01:55
  • 02:21

Worksheet: 11 Questions • 3 Videos

Q1:

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

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?

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?

Q5:

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

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?

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 .

Q9:

Find the maximum or minimum value of the function 𝑓 ( 𝑥 ) = 4 𝑥 + 8 , given 𝑥 [ 3 , 3 ] .

Q10:

Find the maximum or minimum value of the function 𝑓 ( 𝑥 ) = 9 𝑥 6 , given 𝑥 [ 3 , 3 ] .

Q11:

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

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