Given f x = 2 x 2 − 12 x + 16 , a. Write the equation in vertex form: f x = a x − h 2 + k . b. Determine whether the parabola opens upward or downward. c. Identify the vertex. d. Identify the x -intercepts. e. Identify the y -intercepts. f. Sketch the function. g. Determine the axis of symmetry. h. Determine the minimum or maximum value of the function. i. State the domain and range.
Given f x = 2 x 2 − 12 x + 16 , a. Write the equation in vertex form: f x = a x − h 2 + k . b. Determine whether the parabola opens upward or downward. c. Identify the vertex. d. Identify the x -intercepts. e. Identify the y -intercepts. f. Sketch the function. g. Determine the axis of symmetry. h. Determine the minimum or maximum value of the function. i. State the domain and range.
Solution Summary: The author calculates the vertex form of the given equation f(x) = 2x+2-12x +16 by calculating the square.
HW: The frame shown in the figure is pinned at A and
C. Use moment distribution method, with and without
modifications, to draw NFD, SFD, and BMD.
B
I
I
40 kN/m
A
3 m
4 m
Let the region R be the area enclosed by the function f(x)= = 3x² and g(x) = 4x. If the region R is the
base of a solid such that each cross section perpendicular to the x-axis is an isosceles right triangle with a
leg in the region R, find the volume of the solid. You may use a calculator and round to the nearest
thousandth.
y
11
10
9
00
8
7
9
5
4
3
2
1
-1
-1
x
1
2
Let the region R be the area enclosed by the function f(x) = ex — 1, the horizontal line y = -4 and
the vertical lines x = 0 and x = 3. Find the volume of the solid generated when the region R is revolved
about the line y = -4. You may use a calculator and round to the nearest thousandth.
20
15
10
5
y
I
I
I
|
I
+
-1.5
-1
-0.5
0.5
1
1.5
2
2.5
3
-5
I
-10
-15
I
+
I
I
T
I
I
+
-20
I
+
-25
I
I
I
-30
I
3.5
4
x
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus 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