Question

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 of y = f(x). (d) Sketch a graph
of y = f(x). (e) Determine the domain and range of f(x).

Answer #1

Consider the polynomial function P, given by
P(x) =−1/2x^3 - 1/2x^2 + 15x
Sketch a graph of y = P(x) by: determining the zeros of P,
identifying the y-intercept of y = P(x), using test points to
examine the sign of y = P(x) to either side of each zero and
deducing the end behaviour of the polynomial.

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...

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.

[5 point] 1. Examine the quadratic relation y = -2x2 + 16x –
30.
a) Express the relation in factored form. Show your
steps.
b) Determine the zeros.
c) Determine the coordinates of the vertex.
d) Determine the y-intercept.
e) Sketch the graph of the relation.
[5 point] 2. Examine the quadratic relation y = 4x2 – 4x +
1.
a) Express the relation in factored form.
b) Determine the zeros.
c) Determine the coordinates of the vertex.
d) Determine...

Graph f(x)=
x3-x2-16x+16/2x2-18
List and mark the vertical and horizontal asymptotes, oblique
asymptotes, zeros, and y- intercepts on the graph.

Find traits and sketch the graph the equation
for a function g ( x ) that shifts the function f ( x ) = x + 4 x 2
− 16 two units right. Label and scale your
axes.
Domain:
x – Intercepts:
y – Intercept:
Vertical Asymptotes:
Holes:
End Behavior:
Range:

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.

Given the polynomial function f(x)=(x-a)(x-b)^2, and
a<0<b, find the following:
A). Sketch the graph
B). find the x and the y intercepts
C). find the solution to f(x)<0
D). find the solution to f(x) is greater than or equal to 0

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.

Sketch the graph of the function f(x) = x3 +
3x2 +3x + 5

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