Question

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 of the graph of y = f(x). (iv) Sketch a graph of y = −x2 + 6x−8 clearly labelling the vertex of the parabola, along with any intercepts with the x- and y-axes

Answer #1

(i) Graph is below:

This is concave down.

(ii)

Vertex is at

(iii) X intercepts are at

So are the X-intercepts

Y intercepts are

Only Y-intercept is

(iv) Graph with everything labelled:

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.

Question 1a Consider the polynomial function P(x) = x3+x2−20x.
Sketch a graph of y = P(x) by: determining the zeros of P(x),
identifying the y-intercept of y = P(x), using test points to
examine the sign of P(x) to either side of each zero and deducing
the end behaviour of the polynomial.
b Consider the quadratic function f(x) = 2x2 + 8x−1. (a) Express
f(x) in standard form. (b) Determine the vertex of f(x). (c)
Determine the x- and y-intercepts...

1)Find the vertex and the x-intercepts (if any) of the
parabola. (If an answer does not exist, enter DNE.)
f(x) = 3x2 − 5x − 2
vertex
(x, y)
=
x-intercept
(x, y)
=
(smaller x-value)
x-intercept
(x, y)
=
(larger x-value)
Sketch the parabola.
2)Find the vertex and the x-intercepts (if any) of the
parabola. (If an answer does not exist, enter DNE.)
f(x) = x2 + 4x + 4
vertex
(x, y)
=
x-intercept...

Consider the function f(x)=ln(x2
+4)[6+6+8=16 marks]
Note: f'(x) = 2x divided by (x2 +4) f''(x ) =
2(4-x2) divided by (x2+4)2 (I was
unable to put divide sign)
a) On which intervals is increasing or decreasing?
b) On which intervals is concave up or down?
c) Sketch the graph of f(x) Label any intercepts, asymptotes,
relative minima, relative maxima and inflection points.

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.

Consider the function f(x)=ln(x2
+4)[6+6+8=16 marks]
Note: f'(x) = 2x divided by (x2 +4) f''(x ) =
2(4-x2) divided by (x2+4) (I was unable to
put divide sign)
a) On which intervals is increasing or decreasing?
b) On which intervals is concave up or down?
c) Sketch the graph of below. Label any intercepts, asymptotes,
relative minima, relative maxima and inflection points.
.

A quadratic function is given:
f(x)=x2 + 4x − 2
a) express f in standard form (I already got that and it was
(x+2)^2-6
b) sketch a graph of f
c) Find the maximum or minimum value of f. Is this value a
maximum or minimum value?

For the function
f(x) =x(x−4)^3
•
Find all
x-intercepts and find the
y-intercept
•
Find all critical numbers,
•
Determine where the function is increasing and where it is
decreasing,
•
Find and classify the relative extrema,
•
Determine where the function is concave up and where it is
concave down,
•
Find any inflection points, and Use this information to sketch
the graph of the function.
•
Use this information to sketch the graph of the function.

given that f'(x)=-3x^2 -6x answer the following
what inteeval is f(x) increasing or decreasinf
find x coordinates of all inflection points of f(x)
on what interval is f(x) concave up and down
suppose (-2,0), (1,0) and (0,4) are intercepts of f(x) whose
domain is all real. sketch a possible graph of f(x)
find f(x) by integrating f'(x) and intercept information from
above
find all global extrema on interval [-1,5]
show work please and thanks in advance :)

given the polynomial function f(x)=x^2(x-3)(x+1)
find x and y intercepts of f(x) and determine whether the
graph of f crosses or touches the x-axis at each x-intercept.

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