College Algebra

1. Which of the following best describes how the graph of f can be obtained from the graph of y = 1/x^2? f(x) = 4/x^2
a. vertical stretch by a factor of -4
b. horizontal shift of 4 units to the right
c. reflection over the y-axis, vertical shrink by a factor of 4
d. reflection over the x-axis, vertical stretch by a factor of 4
2. Determine the quadratic function f whose vertex is (3, -2) and passes through (2,1).
I have to type the answer in the form of f(x) = ax^2 + bx + c.
I would gladly appreciate the help.

  1. 👍 0
  2. 👎 0
  3. 👁 258
  1. 1. you must have a typo. If f(x) = -4/x^2, then (d). Otherwise, none of the above. (a) would also be technically correct, but we don't usually denote stretching by negative values.

    2. You know that

    y = a(x-3)^2 - 2
    so, plug in your point:
    1 = a(2-3)^2 - 2
    a = 3

    so, y = 3(x-3)^2 - 2
    = 3(x^2 - 6x + 9) - 2
    = 3x^2 - 18x + 25

    1. 👍 0
    2. 👎 0

Respond to this Question

First Name

Your Response

Similar Questions

  1. Calculus

    The graph of f ′(x) is continuous and decreasing with an x-intercept at x = 0. Which of the following statements is false? (4 points) The graph of f has an inflection point at x = 0. The graph of f has a relative maximum at x =

    asked by Henry on February 20, 2016
  2. Calculus really quick check

    The graph of f ′(x) is continuous and decreasing with an x-intercept at x = 2. Which of the following statements must be true? Edit The graph of f has an inflection point at x = 2. The graph of f has a relative maximum at x = 2.

    asked by Ke$ha on May 22, 2017
  3. Algebra 1 Honors

    Which of the following statements best describes the effect of replacing the graph of f(x) with the graph of f(x) − 5? The graph shifts 5 units up. The graph shifts 5 units down. The graph shifts 5 units left. The graph shifts 5

    asked by Mina on October 5, 2016
  4. Algebra

    Given the functions f(x)=1x−2+1 and g(x)=1x+5+9 . Which statement describes the transformation of the graph of function f onto the graph of function g? The graph shifts 8 units right and 7 units down The graph shifts 7 units

    asked by Esther on April 9, 2018
  1. mathematics

    f(x) = 4x^2 − 7x − 15 Part A: What are the x-intercepts of the graph of f(x)? Show your work. Part B: Is the vertex of the graph of f(x) going to be a maximum or minimum? What are the coordinates of the vertex? Justify your

    asked by dingdong on May 5, 2020
  2. English

    Which answer most accurately describes how the author introduces the three brothers in “The Lost Boys”? She describes them as frightened but determined to look tough. She describes them as overwhelmed but still taking care of

    asked by Quinn on April 16, 2019
  3. Mathematics

    The graph of y = 2^x-3 can be obtained by shifting the graph of y= 2^x a) 3 units to the right b) 3 units to the left c) 3 units up d) 3 units down e) 2 units to the right and 3 units up The equation of the graph that is obtained

    asked by Willie on August 5, 2012
  4. Math

    Which statement best describes the effect of replacing the function f(x) = 2x − 2 with the function g(x) = 2x + 3? The graph shifts 1 units left. The graph shifts 5 units left. The graph shifts 1 unit right. The graph shifts 3

    asked by layla on July 26, 2016
  1. math

    Which of the following statements best describes the effect of replacing the graph of y = f(x) with the graph of y = f(x) − 11? answer choices: The graph of y = f(x) will shift up 11 units. The graph of y = f(x) will shift right

    asked by hey on October 26, 2016
  2. Algebra

    The functions f(x) and g(x) are described below: f(x) = 32x + 8 g(x) = 32x − 9 The graph of g(x) is obtained by shifting down the graph of f(x) by _____ units. Numerical Answers Expected! Answer for Blank 1: „ð Question 11

    asked by Brandon on November 24, 2015
  3. Math

    Which of the following statements best describes the effect of replacing the graph of y = f(x) with the graph of y = f(x) + 20? The graph of y = f(x) will shift left 20 units. The graph of y = f(x) will shift down 20 units. The

    asked by layla on August 4, 2016
  4. algebra

    Part C: What are the steps you would use to graph f(x)? Justify that you can use the answers obtained in Part A and Part B to draw the graph. (5 points) f(x) = −16x2 + 24x + 16

    asked by cheyenne on May 8, 2020

You can view more similar questions or ask a new question.