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any ideas? 4. 16 pts) Find the vertex of the quadratic function (x) = -22-20x+8 by...
the vertex of the quadratic function f(x)=-2x? - 20x+8 by completing the square and writing in the vertex form f(x) = a(x-h)+k.
3. List the vertex form of the quadratic function and state all relevant information. 4. Convert the quadratic form f(x) +3-4 into standard form (le. multiply t out). Then check your solution to example 2. 5. Continuing with example 2, read the questions and solutions. Paying particular attention to part d. How can we find the axis of symmetry (aka the x-value of the vertex)? 6. (Note: we will not be covering 'completing the square' in this class, but feel...
5. (5 pts) a. Write the equation for a rational function r(x) that has a vertical asymptote at x = 8, a horizontal asymptote at y=1, and a y-intercept at (0, -1). #5a: b. Find the x-intercept for your function.
12 (Rational Functions) For each rational function below, find (a) the vertical asymptote(s). (b) the horizontal asymptote. (c) the x-intercept(s). (d) the y-intercept. (e) the graph of the function. 2x-6 (1) y X-2 x-5 (2) y 1+ x2-1 12 (Rational Functions) For each rational function below, find (a) the vertical asymptote(s). (b) the horizontal asymptote. (c) the x-intercept(s). (d) the y-intercept. (e) the graph of the function. 2x-6 (1) y X-2 x-5 (2) y 1+ x2-1
3. Determine an equation of a rational function of the form f(x)= ar+b cx+d with x-intercept of 1/4, y-intercept of -1/2, vertical asymptote at x =-2/3, and horizontal asymptote at y = 4/3.
Consider the quadratic function: f(x) = 22? + 14x + 13 . Find the following for this parabola. A) The line of symmetry: B) The vertex: C) The vertical intercept is the point D) Give the coordinates of the two z intercepts of the parabola as ordered pairs. Round your values to two decimal places for this part, if the roots are irrational.
(10 pts ea) In Exercises 1 - 4, for the given rational function f: Find the domain off. Identify any vertical asymptotes of the graph of y = f(x). Identify any holes in the graph. Find the horizontal asymptote, if it exists. Find the slant asymptote, if it exists. 1) f(x) = ***
7. For each function below, find the intercept(s) (if any) and asymptote(s) (both horizontal and vertical, if any), and then sketch the graph with- out using a calculator; you must properly mark/label the ares, all in- tercept(s), horizontal or vertical asymptote(s) to get full credits: (i) y = 22-1 – 2 (ii) y=1- log2 (x + 2) x-intercept: 2-intercept: y-intercept: y-intercept: Asymptote: Asymptote: Graph: Graph:
21. 8 pts For the function g(x) = = 4x2-1 214x A. Find the horizontal asymptote. B. Find the vertical asymptote(s). 0. Find the x intercept(s). D. Solve g(x) <0. Use interval notation. E. Graph g(x)
For the following function, find the hole, x-intercept, y-intercept, vertical asymptote, horizontal asymptote, and oblique asymptote. If something doesn't exist, enter NONE (in all caps). $(x) = 42 hole (,Y):( x-intercept (x, y):( , y-intercept (x, y):( vertical asymptote: vertical asymptote: horizontal asymptote: oblique asymptote: