Just as two points are two pieces of information that uniquely determine a line, a quadratic function is uniquely determined by three pieces of information. The three pieces of information can be three points, or the values of the three coefficients that appear in the standard form of the function, f(x) = a(x - h)² + k, or the expanded form, f(x) = ax² + bx+c. Changing the values of any of the coefficients in either form changes the function and its graph. Click here to access the Explore It in a new window. Suppose you need to find a quadratic function that has x-intercepts at x = 0 and x = 4 and a maximum value of 8. (a) A function in standard form that has parameters a = -1 and k = (b) To obtain intercepts that are separated by 4 units, change the value of a from part (a) to a = (c) To shift the x-intercepts to x = 0 and x = 4, set h to h = has a maximum value of (d) Then, in the standard form equation of the quadratic function, the values of the parameters that meet the given criteria ar a = h = k = (e) In the expanded form equation of the quadratic function, the values of the parameters that meet the given criteria are a = b = C =
Just as two points are two pieces of information that uniquely determine a line, a quadratic function is uniquely determined by three pieces of information. The three pieces of information can be three points, or the values of the three coefficients that appear in the standard form of the function, f(x) = a(x - h)² + k, or the expanded form, f(x) = ax² + bx+c. Changing the values of any of the coefficients in either form changes the function and its graph. Click here to access the Explore It in a new window. Suppose you need to find a quadratic function that has x-intercepts at x = 0 and x = 4 and a maximum value of 8. (a) A function in standard form that has parameters a = -1 and k = (b) To obtain intercepts that are separated by 4 units, change the value of a from part (a) to a = (c) To shift the x-intercepts to x = 0 and x = 4, set h to h = has a maximum value of (d) Then, in the standard form equation of the quadratic function, the values of the parameters that meet the given criteria ar a = h = k = (e) In the expanded form equation of the quadratic function, the values of the parameters that meet the given criteria are a = b = C =
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Transcribed Image Text:Just as two points are two pieces of information that uniquely determine a line, a quadratic function is uniquely determined by
three pieces of information. The three pieces of information can be three points, or the values of the three coefficients that
appear in the standard form of the function, f(x) = a(x - h)² + k, or the expanded form, f(x) = ax² + bx+c. Changing the values of
any of the coefficients in either form changes the function and its graph.
Click here to access the Explore It in a new window.
Suppose you need to find a quadratic function that has x-intercepts at x = 0 and x = 4 and a maximum value of 8.
(a) A function in standard form that has parameters a = -1
and k =
(b) To obtain intercepts that are separated by 4 units, change the value of a from part (a) to
a =
(c) To shift the x-intercepts to x = 0 and x = 4, set h to
h =
has a maximum value of
(d) Then, in the standard form equation of the quadratic function, the values of the parameters that meet the given criteria are
a =
h =
k =
(e) In the expanded form equation of the quadratic function, the values of the parameters that meet the given criteria are
a =
b =
C =
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