# Category : Science and Education

Archive : AYRFCAL1.ZIP

Filename : CI_9.HLP

Review of Curves.

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About 5O% of a typical calculus course deals with curve-sketching. If you

don't know the properties of simple curves, you will have trouble with the

more involved ones! The following are properties of the simple curves.

The equation of a straight line with slope m, and y-intercept b is

y = mx + b .

The equation of a straight line with slope m, passing through the

point x = x , y = y , is

ø ø

y - y = m(x - x ) .

ø ø

The straight lines y = m x + b and y = m x + b intersect

1 1 2 2

at right angles if

m m = -1 .

1 2

The equation of a circle, radius r, center x = x , y = y , is

ø ø

2 2 2

(x - x ) + (y - y ) = r .

ø ø

The equation of a parabola with axis parallel to the y-axis is

2

y = ax + bx + c .

If a > O, the parabola opens upwards.

If a < O, the parabola opens downwards.

The vertex of the parabola is at x = -b/2a.

The equation of a parabola which crosses the x-axis at x = a, x = b, is

y = c(x - a)(x - b) .

The equation of a parabola with axis parallel to the x-axis is

2

x = ay + by + c .

If a > O, the parabola opens to the right.

If a < O, the parabola opens to the left.

The equation of a cubic is

3 2

y = ax + bx + cx + d .

If a > O, the cubic starts in the 3rd quadrant and ends in the 1st.

If a < O, the cubic starts in the 2nd quadrant and ends in the 4th.

The equation of a cubic which crosses the x-axis at x = a, x = b, x = c is

y = d(x - a)(x - b)(x - c) .

Two curves, y = f(x) and y = g(x), intersect at x = x , if

ø

f(x ) = g(x ) .

ø ø

This is the end of the help file. Press the ESC key to return to the quiz

question you were doing.

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