# Worksheet: Quadratic Functions in Different Forms

In this worksheet, we will practice evaluating and writing a quadratic function in different forms.

Q1:

Rewrite the expression in the form .

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• B
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What is the minimum value of the function ?

Q2:

Find the vertex of the graph of .

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Q3:

Find the vertex of the graph of .

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Q4:

Consider the graph: Which is the following is the same as the function whose graph is shown?

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Q5:

Determine the quadratic function with the following properties:

• its graph has a vertex at
• A
• B
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• DThe function does not exist.
• E

Q6:

By writing in vertex form, find such that has exactly one solution.

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Q7:

Consider the function where . What is the -coordinate of the vertex of its curve?

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Q8:

Find the vertex of the graph of .

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Q9:

Rewrite the expression in the form .

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• E

What is the minimum value of the function ?

Q10:

Rewrite the expression in the form .

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What is the minimum value of the function ?

Q11:

Rewrite the expression in the form .

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What is the maximum value of the function ?

Q12:

In completing the square for quadratic function , you arrive at the expression . What is the value of ?

Q13:

Which of the following is the vertex form of the function ?

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Q14:

Find the vertex of the graph of .

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Q15:

Find the vertex of the graph of .

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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 , find the area of the figure included between the -axis and the curve of the quadratic function in square units. • A32 square units
• B square units
• C square units
• D square units

Q17:

Find the coordinates of the vertex of the curve .

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Q18:

In the figure below, the area included between the curve of the quadratic function and the line segment lying on the is calculated by the relation . Represent the function on the same lattice to find the area of the part included between the two functions in area units. • A23 square units
• B13 square units
• C27 square units
• D5 square units

Q19:

The figure below represents the function . Find the area of triangle given . Q20:

Two siblings are 3 years apart in age. Write an equation for , the product of their ages, in terms of , the age of the younger sibling.

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Q21:

A cell phone company has the following cost and revenue functions: and , where is the number of cell phones. State the range for the number of cell phones they can produce while making a profit. Round your answers to the nearest integer that guarantees a profit.

• A28–70 cell phones
• BMore than 160 cell phones
• C28–71 cell phones
• D27–70 cell phones