Lesson 5 Vocab

Lesson 5 Vocab

By Jeff Simmons

​Please open your Carnegie Learning to Lesson 5: Activity 5.1 ....

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These slides follow the lesson​

In this lesson, you will explore a parabola as a locus of points to determine more information about the parabola.

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NOTE: All underlined words are in the questions.​

​​Activity 5.1​: A Parabola as a Locus of points

A locus of points is a set of points that share a property. A parabola is the set of all points in a plane that are equidistant from both a focus and a directrix. The focus is a point which lies inside the parabola on the axis of symmetry. The directrix is a line that is perpendicular to the axis of symmetry and lies outside the parabola and does not intersect the parabola.

Keywords:

  Everything you already know about parabolas remains true. The axis of symmetry of a parabola is a line that passes through the parabola and divides it into two symmetrical parts that are mirror images of each other.

ACTIVITY 5.1: A Parabola as a Locus of Points

Remember:

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The concavity of a parabola describes the orientation of the curvature of the parabola. A parabola can be concave up, concave down, concave right, or concave left, as shown.

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​ACTIVITY 5.1: A Parabola as a Locus of Points - Question 2

​Concavity:

Multiple Choice

Which of these parabolas is concave down?

Multiple Choice

Which of these parabolas is concave left?

Multiple Choice

Which of these parabolas is concave right?

Multiple Choice

Which of these parabolas is concave up?

is the point on the axis of symmetry which is exactly midway between the focus and the directrix. It is also the point where the parabola changes direction.

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ACTIVITY 5.1: A Parabola as a Locus of Points: Question 2

The vertex of a parabola:

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Multiple Select

What can you call the highest point of a concave down parabola.

[choose ALL correct answers]

• directrix

• focus

• maximum

• minimum

• vertex

Multiple Select

What can you call the lowest point of a concave up parabola.

[choose ALL correct answers]

• directrix

• focus

• maximum

• minimum

• vertex

Multiple Choice

What can you call a point which lies inside the parabola on the axis of symmetry.

• directrix

• focus

• maximum

• minimum

• vertex

Multiple Choice

What can you call a line that is perpendicular to the axis of symmetry and lies outside the parabola and does not intersect the parabola.

• directrix

• focus

• maximum

• minimum

• vertex

Multiple Choice

A parabola is the set of all points equidistant from the focus and the directrix.

• true
• false

Multiple Choice

The focus is always inside the parabola.

• true
• false

Multiple Choice

The vertex, (h, k), is halfway between the focus and the directrix.

• true
• false

Multiple Choice

Given the equation for this parabola:
 y=-(x-4)²-3,
does this parabola have a maximum or minimum value?

• Maximum
• Minimum

Multiple Choice

What is the point inside the parabola 'p' units from the vertex?

• vertex
• focus
• directrix
• axis of symmetry

Multiple Choice

All parabolas with a vertical directrix open the left or right.

• true
• false

Multiple Choice

The directrix is parallel to the axis of symmetry.

• True

• False

Feel free to take this again for a higher grade...

End of vocab practice