# Worksheet: Quadratic Functions in Different Forms

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

**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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**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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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.

- A28β70 cell phones
- BMore than 160 cell phones
- C28β71 cell phones
- D27β70 cell phones