In the following exercises, (a) graph the quadratic functions on the same rectangular coordinate system and (b) describe what effect adding a constant, h , to the function has on the basic parabola. 301. f ( x ) = x 2 , g ( x ) = ( x − 3 ) 2 , and h ( x ) = ( x + 3 ) 2 .
In the following exercises, (a) graph the quadratic functions on the same rectangular coordinate system and (b) describe what effect adding a constant, h , to the function has on the basic parabola. 301. f ( x ) = x 2 , g ( x ) = ( x − 3 ) 2 , and h ( x ) = ( x + 3 ) 2 .
In the following exercises, (a) graph the quadratic functions on the same rectangular coordinate system and (b) describe what effect adding a constant, h, to the function has on the basic parabola.
301.
f
(
x
)
=
x
2
,
g
(
x
)
=
(
x
−
3
)
2
,
and
h
(
x
)
=
(
x
+
3
)
2
.
System that uses coordinates to uniquely determine the position of points. The most common coordinate system is the Cartesian system, where points are given by distance along a horizontal x-axis and vertical y-axis from the origin. A polar coordinate system locates a point by its direction relative to a reference direction and its distance from a given point. In three dimensions, it leads to cylindrical and spherical coordinates.
A human slingshot was used to launch a stunt man into the air across two football fields where he landed into a safety foam pit which was ground level. The trajectory of the stunt man can be modeled by the equation h(t)=-16t^2+144t, where h(t) is height in feet and t is time in seconds (if air resistance is neglected) How long will it take the stunt man to reach the ground?
Find the domain of f(x) = 28 - 2x.
Antoine stands on a balcony and throws a ball to his dog, who is at
ground level. The ball's height (in meters above the ground), x seconds
after Antoine threw it, is modeled by: h(x)=-2x² + 4x + 16. The maximum
of the ball will reach 20 feet high after it travels a horizontal distance of 8
ft. Will the ball reach the dog's mouth if the dog is 15 feet away and
doesn't move at all? Explain your reasoning.
8
15 ft.
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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