Lesson 4 Directing Our Focus Develop Understanding

Ready

Graph each set of functions on the same coordinate axes. Describe in what way the graphs are the same and in what way they are different.

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Set

The points , , , , , , and the origin, , have been identified on the diagram. In addition, the dotted lines , , , , and have been graphed to remind you that the points you are seeking lie somewhere on those lines. Let point be the focus and the line be the directrix.

Graph with F(0,1), D(0,-1), (1,y1) (2,y2) (3,y3) (4,y3) and dotted lines x=-1, 1,2,3,4 x–4–4–4–3–3–3–2–2–2–1–1–1111222333444555y–1–1–1111222333444000

5.

The geometric definition of a parabola states that the distance from the focus to a point that lies on the parabola and the distance from point to the directrix must be equal.

According to this definition, is the point a point on the parabola that is being constructed in the diagram? Justify your answer.

6.

The points , , , and have not been labeled with ordered pairs in the diagram. Write the coordinates of , , , and .

7.

Use a straightedge to draw a line segment from to . Then draw a vertical line segment from to the line . What should the two line segments have in common?

Line y=-1, F(0,1) line x=1 and point (1,y1) x111y–1–1–1111000

8.

Write an equation that relates the lengths of the two line segments, and calculate the distance from to and the distance from to the line .

9.

What is the value of in the point identified as ?

10.

What are the missing values of , , and in the ordered pairs shown on the diagram?

11.

Write the equation of this parabola for any value of using the geometric definition.

Use the point .

Let be any point of the parabola and be the distance from to the directrix.

Go

Use completing the square to find the center and radius of the circle.

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