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. 302. f ( x ) = x 2 , g ( x ) = ( x + 4 ) 2 , and h ( x ) = ( x − 4 ) 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. 302. f ( x ) = x 2 , g ( x ) = ( x + 4 ) 2 , and h ( x ) = ( x − 4 ) 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.
302.
f
(
x
)
=
x
2
,
g
(
x
)
=
(
x
+
4
)
2
,
and
h
(
x
)
=
(
x
−
4
)
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.
Given the quadratic function f(x) = (x+2)^2-5
Find the y-intercept
For the month of May, the number of mosquitoes hatched over 2 weeks in Minneapolis, Minnesota ( in y = millions of mosquitoes) as a function of rainfall (in x = centimeters) is modeled with a vertex at (5 , 25). So, y = - 1 ( x - 5 )^2 + 25. Use the vertex equation to find how much rain will produce 9 million mosquitoes.
Consider the quadratic function q(x) = x 2 + 6x − 16. Respond to the following (in any order):
(a) Show how to locate the coordinates of the vertex.
(b) Write an equation for the axis of symmetry.
(c) Determine the x-intercepts and the y-intercept exactly.
(d) Sketch a graph of the function showing the vertex, axis of symmetry, x-intercepts, and y-intercept.
(e) Write an equation for the function, p, that results from shifting the graph of the function q to the left 4 units and up 3 units.
(f) Graph the function p on the same axes as the function q.
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