# 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

Q11:

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

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

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 .

 𝑥 𝑓(𝑥) −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 .

 𝑥 𝑓(𝑥) 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 .

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.

• 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