Answer Problems 83 and 84 using the following: A quadratic function of the form f ( x ) = a x 2 + b x + c with b 2 − 4 a c > 0 may also be written in the form f ( x ) = a ( x – r 1 ) ( x − r 2 ) , where r 1 and r 2 are the x -intercepts of the graph of the quadratic function. (a) Find a quadratic function whose x -intercepts are − 5 and 3 with a = 1 ; a = 2 ; a = − 2 ; a = 5 . (b) How does the value of a affect the intercepts? (c) How does the value of a affect the axis of symmetry? (d) How does the value of a affect the vertex? (e) Compare the x -coordinate of the vertex with the midpoint of the x -intercepts . What might you conclude?
Answer Problems 83 and 84 using the following: A quadratic function of the form f ( x ) = a x 2 + b x + c with b 2 − 4 a c > 0 may also be written in the form f ( x ) = a ( x – r 1 ) ( x − r 2 ) , where r 1 and r 2 are the x -intercepts of the graph of the quadratic function. (a) Find a quadratic function whose x -intercepts are − 5 and 3 with a = 1 ; a = 2 ; a = − 2 ; a = 5 . (b) How does the value of a affect the intercepts? (c) How does the value of a affect the axis of symmetry? (d) How does the value of a affect the vertex? (e) Compare the x -coordinate of the vertex with the midpoint of the x -intercepts . What might you conclude?
Solution Summary: The author explains that the x-coordinate of the vertex and axis of symmetry are all the same.
Answer Problems 83 and 84 using the following: A quadratic function of the form
with
may also be written in the form
, where
are the
of the graph of the quadratic function.
(a) Find a quadratic function whose
are
and 3 with
.
(b) How does the value of
affect the intercepts?
(c) How does the value of
affect the axis of symmetry?
(d) How does the value of
affect the vertex?
(e) Compare the
of the vertex with the midpoint of the
. What might you conclude?
Evaluate the triple integral
3'
23
HIG
2
+3
f(x, y, z)dxdydz where f(x, y, z) = x +
2x-y
ม
u =
v =
and w =
2
2
3
Triple Integral
Region R
-2
x
N
2
y
3
Find the volume of the solid bounded below by the circular cone z = 2.5√√√x² + y² and above by the
sphere x² + y²+z² = 6.5z.
Electric charge is distributed over the triangular region D shown below so that the charge density at (x, y)
is σ(x, y) = 4xy, measured in coulumbs per square meter (C/m²). Find the total charge on D. Round
your answer to four decimal places.
1
U
5
4
3
2
1
1
2
5
7
coulumbs
Chapter 3 Solutions
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Differential Equation | MIT 18.01SC Single Variable Calculus, Fall 2010; Author: MIT OpenCourseWare;https://www.youtube.com/watch?v=HaOHUfymsuk;License: Standard YouTube License, CC-BY