a. Show that the points 2 , 9 , − 1 , − 6 , and − 4 , − 3 are not collinear by finding the slope between 2 , 9 and − 1 , − 6 , and the slope between 2 , 9 and − 4 , − 3 . b. Find an equation of the form y = a x 2 + b x + c that defines the parabola through the points. c. Use a graphing utility to verify that the graph of the equation in part (b) passes through the given points.
a. Show that the points 2 , 9 , − 1 , − 6 , and − 4 , − 3 are not collinear by finding the slope between 2 , 9 and − 1 , − 6 , and the slope between 2 , 9 and − 4 , − 3 . b. Find an equation of the form y = a x 2 + b x + c that defines the parabola through the points. c. Use a graphing utility to verify that the graph of the equation in part (b) passes through the given points.
Solution Summary: The author proves that the given points are not collinear by finding the slope between them.
a. Show that the points
2
,
9
,
−
1
,
−
6
,
and
−
4
,
−
3
are not collinear by finding the slope between
2
,
9
and
−
1
,
−
6
, and the slope between
2
,
9
and
−
4
,
−
3
.
b. Find an equation of the form
y
=
a
x
2
+
b
x
+
c
that defines the parabola through the points.
c. Use a graphing utility to verify that the graph of the equation in part (b) passes through the given points.
University Calculus: Early Transcendentals (3rd Edition)
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