# Worksheet: Features of Quadratic Functions

In this worksheet, we will practice identifying features of quadratic functions, such as its vertex, extrema, 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.

- AThe vertex is , the value of the function at the vertex is 3, it is a maximum value.
- BThe vertex is , the value of the function at the vertex is , it is a minimum value.
- CThe vertex is , the value of the function at the vertex is 3, it is a minimum value.
- DThe vertex is , the value of the function at the vertex is , it is a minimum value.
- EThe 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 .

- AThe domain is , and the range is .
- BThe domain is , and the range is .
- CThe domain is , and the range is .
- DThe domain is , and the range is .
- EThe domain is , and the range is .

**Q7: **

Determine the domain and the range of the function .

- AThe domain is , and the range is .
- BThe domain is , and the range is .
- CThe domain is , and the range is .
- DThe domain is , and the range is .
- EThe 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 blue graph
- Bthe yellow graph
- Cthe red 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 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

**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 blue graph
- Bthe red 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

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

**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
- BThe function does not exist.
- C
- D
- E

**Q17: **

A stone is projected vertically upward. 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 .

**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.

- AThe vertex is , the value of the function at the vertex is , it is a maximum value.
- BThe vertex is , the value of the function at the vertex is 1, it is a minimum value.
- CThe vertex is , the value of the function at the vertex is , it is a minimum value.
- DThe vertex is , the value of the function at the vertex is 1, it is a minimum value.
- EThe 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.

- AThe vertex is , the value of the function at the vertex is 1, it is a minimum value.
- BThe vertex is , the value of the function at the vertex is 3, it is a maximum value.
- CThe vertex is , the value of the function at the vertex is 1, it is a maximum value.
- DThe vertex is , the value of the function at the vertex is 3, it is a maximum value.
- EThe 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

**Q23: **

Let and be the function whose graph is shown.

Which of the following statements is true?

- AThe minimum value of is greater than the maximum value of .
- BThe sums of zeros of the two functions are the same.
- COn the interval , function has the higher average rate of change.
- DOn the interval , function has the lower average rate of change.
- EBoth functions have the same axis of symmetry.

**Q24: **

A quadratic function has distinct positive roots. Which of the following must be true about its graph?

- AThe parabola must be concave up.
- BThe axis of symmetry must be for a positive value .
- CThe axis of symmetry must be for a positive value .
- DIts vertex must be above the -axis.
- EThe parabola must be concave down.

**Q25: **

Is any quadratic function a nonlinear function?

- Ano
- Byes