Page 101 - Calc for the Clueless

Given y = -7x. Sketch. Label vertex, focus, directrix.
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From the chart, we know the sketch is picture 4. Now let 4c = 7 (ignore the minus sign), c = 7/4. The vertex is
(0,0). The focus is (-7/4,0), because it is on the x axis to the left of the origin. The directrix is y = 7/4; y, a
vertical line, = +7/4 because it is to the right of the origin.

Example 14—

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Sketch (y- 3) = -7(x + 2).
To understand the following, we need only note the difference between x + y = 25 and (x- 3) + (y + 6) = 25.
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Has the shape changed? No. Has the radius changed? No. What has changed? The center. Instead of being at the
point (0,0), the center is at the point (3,-6).
In the case of the parabola, what has changed is the vertex. Instead of being at the point (0,0), the vertex is at
the point (-2,3). The shape is the same. 4c still equals 7. So c = 7/4. The focus now becomes (-2 -7/4,3), 7/4 to
the left of the vertex (-7/4 from the x coordinate). The directrix is x = -2 + 7/4.

Example 15—

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Sketch the parabola 2x + 8x + 6y + 10 + 0.
Original.

Divide through by the coefficient of the squared variable.

On one side, get all the terms that have the squared letter; everything else goes to the other
side.

Complete the square; add to both
sides.

Factor and simplify.