Question

Graph the quadratic function f x( ) = −2x 2 + 6x − 3. Give the vertex, axis, x-intercepts, y-intercept, domain, range, and intervals of the domain for which the function is increasing or decreasing.

Answer #1

Let f(x)= 3x^2-6x+1. Express this quadratic function in the
standard form . Find the vertex, the minimum or maximum value of
function , x-intercepts, y-intercept, domain and range. Show your
table of values, and sketch the graph.

Consider the quadratic function f, given by f(x) = −x2 + 6x−8.
(i) Determine if the graph of y = −x2 + 6x − 8 is concave up or
concave down, providing a justiﬁcation with your answer. (ii)
Re-write the equation of the quadratic function f, given by f(x) =
−x2 +6x−8, in the standard form f(x) = a(x−h)2+k by completing the
square. Hence determine the vertex of the graph of y = f(x).
(iii) Identify the x-intercepts and y-intercept...

For the equation
?f(x)equals=x squared minus 2 x minus 15x2?2x?15?,
?a) determine whether the graph of the given
quadratic function opens up or? down, ?b) find
the? vertex, ?c) find the axis of? symmetry,
?d) find the? x- and? y-intercepts, and
?e) sketch the graph of the function.

For the rational function f(x)= (3x^3 - 27x^2 + 60x) / (2x^2 +
2x - 40) find the domain, x-intercepts, y-intercept, and vertical
asymptote/ vertical asymptotes.

Consider the function: f ( x ) = − 3 x 2 + 18 x + 48
The direction of the graph is like which of the following:
The y-intercept is at y =
The x-intercepts are at x =
The vertex is at the point=

Analyze and plot the graph of f(x)= x^4/2 - 2x^3/3. for this,
find;
1) domain of f:
2)Vertical asymptotes:
3) Horizontal asymptotes:
4) Intersection in y:
5) intersection in x:
6) Critical numbers
7) intervals where f is increasing:
8) Intervals where f is decreasing:
9) Relatives extremes
Relatives minimums:
Relatives maximums:
10) Inflection points:
11) Intervals where f is concave upwards:
12) intervals where f is concave down:
13) plot the graph of f on the plane:

Sketch the graph of the function f(x) = x − 4 / x + 4 using the
guidelines below, a. Determine the domain of f.
b. Find the x and y intercepts.
c. Find all horizontal and vertical asymptotes.
d. Determine the intervals of increasing/decreasing.
e. Determine the concavity of f.

Let f(x)=6x^2−2x^4. Find the open intervals on which f is
increasing (decreasing). Then determine the x-coordinates of all
relative maxima (minima).
1.
f is increasing on the intervals
2.
f is decreasing on the intervals
3.
The relative maxima of f occur at x =
4.
The relative minima of f occur at x =

what does a derivative tell us?
F(x)=2x^2-5x-3, [-3,-1]
F(x)=x^2+2x-1, [0,1]
Give the intervals where the function is increasing or
decreasing?
Identify the local maxima and minima
Identify concavity and inflection points

Analyze the function f and sketch the curve of f by hand.
Identify the domain, x-intercepts, y-intercepts, asymptotes,
intervals of increasing, intervals of decreasing, local maximums,
local minimums, concavity, and inflection points. f(x) = 3x^4 −
4x^3 + 2

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