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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.

Q1:

Find the coordinates of the vertex of the function π ( π₯ ) = β 5 + 7 π₯ β π₯ 2 .

Q2:

An object is projected such that it follows a parabolic path given by π¦ = β 0 . 5 π₯ + 8 0 π₯ 2 , where π₯ is the horizontal distance traveled in feet and π¦ 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 π ( π₯ ) = π₯ + 1 0 2 , given π₯ β [ β 3 , 3 ] .

Q4:

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

Q5:

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

Q6:

Find the maximum or minimum value of the function π ( π₯ ) = π₯ β 5 2 , given π₯ β [ β 3 , 3 ] .

Q7:

Find the maximum or minimum value of the function π ( π₯ ) = 3 π₯ β 1 2 π₯ β 2 2 , given π₯ β [ β 1 , 5 ] .

Q8:

Which of these functions has the greatest maximum value?

Q9:

At which value of π₯ does the function π ( 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?

Q11:

The graph π¦ = π ( 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 π ( π₯ ) in vertex form?

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