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In this lesson, we will learn how to write a quadratic function in vertex form.

Q1:

Rewrite the expression π₯ + 1 4 π₯ 2 in the form ( π₯ + π ) + π 2 .

What is the minimum value of the function π ( π₯ ) = π₯ + 1 4 π₯ 2 ?

Q2:

Find the vertex of the graph of π¦ = β π₯ 2 .

Q3:

Find the vertex of the graph of π¦ = 5 ( π₯ + 1 ) + 6 2 .

Q4:

Consider the graph:

Which is the following is the same as the function π ( π₯ ) = β 2 ( π₯ + 1 ) ( π₯ + 5 ) whose graph is shown?

Q5:

Determine the quadratic function π with the following properties:

Q6:

By writing π ( π₯ ) = β π₯ + 8 π₯ + π΄ 2 in vertex form, find π΄ such that π ( π₯ ) = 3 has exactly one solution.

Q7:

Consider the function π ( π₯ ) = π π₯ + π π₯ + π 2 where π β 0 . What is the π₯ -coordinate of the vertex of its curve?

Q8:

Find the vertex of the graph of π¦ = ( π₯ β 3 ) + 2 2 .

Q9:

Rewrite the expression 4 π₯ β 1 2 π₯ + 1 3 2 in the form π ( π₯ + π ) + π 2 .

What is the minimum value of the function π ( π₯ ) = 4 π₯ β 1 2 π₯ + 1 3 2 ?

Q10:

Rewrite the expression π₯ β 1 2 π₯ + 2 0 ο¨ in the form ( π₯ + π ) + π ο¨ .

What is the minimum value of the function π ( π₯ ) = π₯ β 1 2 π₯ + 2 0 ο¨ ?

Q11:

Rewrite the expression β 4 π₯ β 8 π₯ β 1 2 in the form π ( π₯ + π ) + π 2 .

What is the maximum value of the function π ( π₯ ) = β 4 π₯ β 8 π₯ β 1 2 ?

Q12:

In completing the square for quadratic function π ( π₯ ) = π₯ + 1 4 π₯ + 4 6 2 , you arrive at the expression ( π₯ β π ) + π 2 . What is the value of π ?

Q13:

Which of the following is the vertex form of the function π ( π₯ ) = 2 π₯ + 1 2 π₯ + 1 1 2 ?

Q14:

Find the vertex of the graph of π¦ = π₯ + 7 2 .

Q15:

Find the vertex of the graph of π¦ = π₯ 2 .

Q16:

If the area included between the curve of a quadratic function and a horizontal line segment joining any two points lying on it, as shown in the figure below, is calculated by the relation π = 2 3 π π§ , find the area of the figure included between the π₯ -axis and the curve of the quadratic function π ( π₯ ) = π₯ β 1 2 π₯ + 3 2 2 in square units.

Q17:

Find the coordinates of the vertex of the curve π ( π₯ ) = 8 β ( β 4 β π₯ ) 2 .

Q18:

In the figure below, the area included between the curve of the quadratic function π ( π₯ ) = π₯ β 1 6 π₯ + 5 5 2 and the line segment π lying on the π₯ -axis is calculated by the relation π = 2 3 π π§ . Represent the function π ( π₯ ) = | π₯ β 8 | β 3 on the same lattice to find the area of the part included between the two functions in area units.

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