# Worksheet: Features of Quadratic Functions

Q1:

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.

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 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.

Q3:

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.

Q4:

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 .

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:

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

Q7:

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?

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:

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 .

Q10:

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

Q11:

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

• A
• B
• C
• D

Q12:

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

Q13:

Find the coordinates of the vertex of the function .

• A
• B
• C
• D

Q14:

Find the coordinates of the vertex of the function .

• A
• B
• C
• D

Q15:

Find the coordinates of the vertex of the function .

• A
• B
• C
• D

Q16:

Let be the function in the given table and .

 π₯ π ( π₯ ) β4 β3 β2 β1 0 1 2 3 45 21 5 β3 β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.

Q17:

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

Q18:

The shown table is that of quadratic function .

 π₯ π ( π₯ ) 0 1 2 3 4 5 β21 β5 3 3 β5 β21

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

• A
• B
• C
• D
• E

Q19:

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

Q20:

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

Q21:

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 .

Q22:

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 .