# Worksheet: Properties of Parabolas

In this worksheet, we will practice identifying the properties of the parabola using graphical representation and the function rule.

Q1:

Find the coordinates of the vertex of the function .

• A
• B
• C
• D

Q2:

Find the vertex of the graph of .

• A
• B
• C
• D
• E

Q3:

Find the vertex of the graph of .

• A
• B
• C
• D
• E

Q4:

Find the vertex of the graph of .

• A
• B
• C
• D
• E

Q5:

Find the vertex of the graph of .

• A
• B
• C
• D
• E

Q6:

Find the point of symmetry of the curve of the function .

• A
• B
• C
• D

Q7:

Find the vertex of the quadratic equation .

• A
• B
• C
• D
• E

Q8:

Consider the curve shown below.

Which suitable triple , , would make this the graph of ?

• A
• B
• C
• D
• E

Q9:

The figure shows the curve , the dashed line , and its perpendicular .

Determine the coordinates of the two intersections and .

• A ,
• B ,
• C ,
• D ,
• E ,

Q10:

The figure shows the curve , the dashed line , and its perpendicular .

Determine the coordinates of the two intersections and .

• A ,
• B ,
• C ,
• D ,
• E ,

The vertex of this parabola lies where the line meets the parabola at exactly one point.

What is the value of ? What are the coordinates of the vertex?

• A , vertix:
• B , vertix:
• C , vertix:
• D , vertix:
• E , vertix:

The vertex also lies on the line of symmetry , which is present in the equation. It turns out that the equation gives a parabola whose axis of symmetry is parallel to .

By completing the square and rewriting this as , determine what the new axis of symmetry is. What is the value of the constant ?

• A ,
• B ,
• C ,
• D ,
• E ,

By determining , such that , complete the squares and rewrite as . What is this expression? What is the vertex of the parabola?

• A ,
• B ,
• C ,
• D ,
• E ,

Q11:

Consider the parabola with Cartesian equation .

What are the coordinates of its focus?

• A
• B
• C
• D
• E

Write the equation of its directrix.

• A
• B
• C
• D
• E

Q12:

A parabola has the equation .

What are the coordinates of its focus?

• A
• B
• C
• D
• E

Write an equation for its directrix.

• A
• B
• C
• D
• E

Q13:

Consider a parabola described by the parametric equations , , .

What are the coordinates of the focus?

• A
• B
• C
• D
• E

What is the equation of the directrix?

• A
• B
• C
• D
• E

Q14:

A parabola has an equation .

Find the coordinates of the vertex.

• A
• B
• C
• D
• E

Determine the equation of the directrix.

• A
• B
• C
• D
• E

Q15:

Consider the parabola with the Cartesian equation .

What are the coordinates of the focus of the parabola with the Cartesian equation ?

• A
• B
• C
• D
• E

Write the equation of its directrix.

• A
• B
• C
• D
• E

Q16:

Write an equation for the parabola whose focus is the point and whose directrix is the line .

• A
• B
• C
• D
• E

Q17:

Suppose that for some constant . What is the -coordinate of the vertex of parabola ?

• A
• B
• C
• D
• E

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