# Worksheet: Properties of Parabolas

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

**Q2: **

Find the vertex of the graph of .

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**Q3: **

Find the vertex of the graph of .

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**Q4: **

Find the vertex of the graph of .

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**Q5: **

Find the vertex of the graph of .

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**Q6: **

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

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**Q7: **

Find the vertex of the quadratic equation .

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**Q8: **

Consider the curve shown below.

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

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**Q9: **

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

Determine the coordinates of the two intersections and .

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- E ,

**Q10: **

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

Determine the coordinates of the two intersections and .

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- 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 ?

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- 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?

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- B ,
- C ,
- D ,
- E ,

**Q11: **

Consider the parabola with Cartesian equation .

What are the coordinates of its focus?

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Write the equation of its directrix.

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**Q12: **

A parabola has the equation .

What are the coordinates of its focus?

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Write an equation for its directrix.

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**Q13: **

Consider a parabola described by the parametric equations , , .

What are the coordinates of the focus?

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What is the equation of the directrix?

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**Q14: **

A parabola has an equation .

Find the coordinates of the vertex.

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Determine the equation of the directrix.

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**Q15: **

Consider the parabola with the Cartesian equation .

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

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Write the equation of its directrix.

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**Q16: **

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

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**Q17: **

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

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