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 demonstrates that the provided 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.
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, algebra and related others by exploring similar questions and additional content below.
Finding The Focus and Directrix of a Parabola - Conic Sections; Author: The Organic Chemistry Tutor;https://www.youtube.com/watch?v=KYgmOTLbuqE;License: Standard YouTube License, CC-BY