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 − 3 and 1 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 − 3 and 1 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 1 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?
Solve the following graphically.
x + 3 = √12x+1
Ox=2
x = -2 or x = -4
Ox=-4
x = 4 or x = 2
1.Find the following Quadratic functions:
A. Give the equation of a quadratic function that passes through the points (1,3),(0,6),
and (-5,-9)
Average Cost See Problem 71. Suppose that the government imposes a $1000-per-day tax on the bicycle manufacturer so that the daily cost C of manufacturing x bicycles is now given by C(x) = 80x + 6000. Now the average daily cost C is given by C(x) = 80x + 6000/x . How many bicycles must be produced each day for the average cost to be no more than $100?
Chapter 3 Solutions
Precalculus Enhanced with Graphing Utilities (7th Edition)
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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