In this worksheet, we will practice identifying features of quadratic equations, such as its vertex, maximum or minimum value, axis of symmetry, domain, and range.

**Q1: **

Find the coordinates of the vertex of the function .

- A
- B
- C
- D

**Q2: **

Find the coordinates of the vertex of the graph of . State the value of the function at the vertex and determine whether it is a maximum or minimum value.

- A The vertex is , the value of the function at the vertex is , it is a minimum value.
- B The vertex is , the value of the function at the vertex is 3, it is a minimum value.
- C The vertex is , the value of the function at the vertex is 3, it is a maximum value.
- D The vertex is , the value of the function at the vertex is , it is a minimum value.
- E The vertex is , the value of the function at the vertex is , it is a maximum value.

**Q3: **

Find the axis of symmetry of the graph of .

- A
- B
- C
- D
- E

**Q4: **

The graph of the quadratic function intersects the -axis at the points and . What is the -coordinate of the vertex of the graph?

**Q5: **

The graph of the function passes through the point . Given that the minimum value of the function is , and the axis of symmetry is the line , find the the values of , , and .

- A , ,
- B , ,
- C , ,
- D , ,

**Q6: **

Determine the domain and the range of the function .

- A The domain is , and the range is .
- B The domain is , and the range is .
- C The domain is , and the range is .
- D The domain is , and the range is .
- E The domain is , and the range is .

**Q7: **

Determine the domain and the range of the function .

- A The domain is , and the range is .
- B The domain is , and the range is .
- C The domain is , and the range is .
- D The domain is , and the range is .
- E The domain is , and the range is .

**Q8: **

For the function , answer the following questions.

Find, by factoring, the zeros of the function.

- A
- B
- C
- D
- E

Identify the graph of .

- Athe red graph
- Bthe yellow graph
- Cthe blue graph

Write the equation for , the function that describes the yellow graph.

- A
- B
- C
- D
- E

Write the equation for , the function that describes the blue graph.

- A
- B
- C
- D
- E

**Q9: **

For the function , answer the following questions.

Find, by factoring, the zeros of the function.

- A
- B
- C
- D
- E

Identify the graph of .

- Athe red graph
- Bthe blue graph
- Cthe green graph

Write the equation for , the function that describes the blue graph.

- A
- B
- C
- D
- E

Write the equation for , the function that describes the green graph.

- A
- B
- C
- D
- E

**Q10: **

For the function , answer the following questions.

Find, by factoring, the zeros of the function.

- A
- B
- C
- D
- E

Identify the graph of .

- Athe red graph
- Bthe green graph
- Cthe blue graph

Write the equation for , the function that describes the blue graph.

- A
- B
- C
- D
- E

Write the equation for , the function that describes the green graph.

- A
- B
- C
- D
- E

**Q11: **

The following statements refer to the function . Which statement is true?

- AThe range of the function is all positive real numbers.
- BThe function has two roots.
- CThe function has one relative maximum.
- DThe function has a vertex at .

**Q12: **

A ball is hurled upward from the top of a building. Its height in feet at time , in seconds, can be described by the function . How many seconds did it take for the ball to reach its maximum height?

**Q13: **

What are the coordinates of the vertex of the graph of ?

- A
- B
- C
- D

**Q14: **

Let be the function in the given table and .

−4 | −3 | −2 | −1 | 0 | 1 | 2 | 3 | |

45 | 21 | 5 | −3 | −3 | 5 | 21 | 45 |

Which of the following is true?

- AThey have the same zeros.
- BThey are the same function.
- CThey have the same vertex.
- DThey have the same axis of symmetry.
- EThey have the same sum of zeros.

**Q15: **

The shown table is that of quadratic function .

0 | 1 | 2 | 3 | 4 | 5 | |

−21 | −5 | 3 | 3 | −5 | −21 |

Which of the following has an axis of symmetry closest to ?

- A
- B
- C
- D
- E

**Q16: **

Determine the quadratic function with the following properties:

- its graph has a vertex at
- as .

- A
- B
- C
- D The function does not exist.
- E

**Q17: **

A stone is projected vertically upwards. Its height above the ground after seconds is given by Find the maximum height the stone reaches.

**Q18: **

The function intersects the -axis at the point . Find the value of .

**Q19: **

An object’s height in feet, , is the function of the horizontal distance traveled, feet, from where it is projected. What is the maximum height of this motion?

**Q20: **

Find the coordinates of the vertex of the graph of . State the value of the function at the vertex and determine whether it is a maximum or minimum value.

- A The vertex is , the value of the function at the vertex is 1, it is a minimum value.
- B The vertex is , the value of the function at the vertex is , it is a minimum value.
- C The vertex is , the value of the function at the vertex is , it is a maximum value.
- D The vertex is , the value of the function at the vertex is 1, it is a minimum value.
- E The vertex is , the value of the function at the vertex is 1, it is a maximum value.

**Q21: **

Find the coordinates of the vertex of the graph of . State the value of the function at the vertex and determine whether it is a maximum or minimum value.

- A The vertex is , the value of the function at the vertex is 3, it is a maximum value.
- B The vertex is , the value of the function at the vertex is 1, it is a maximum value.
- C The vertex is , the value of the function at the vertex is 1, it is a minimum value.
- D The vertex is , the value of the function at the vertex is 3, it is a maximum value.
- E The vertex is , the value of the function at the vertex is 3, it is a minimum value.

**Q22: **

Find the coordinates of the vertex of the function .

- A
- B
- C
- D