Question

find the values of a,b and c for the quadratic polynomial f(x)=
ax^{2}+bx+c which best fits the function h(x)=w^2x+1 at
x=0

f(0)=h(0), and f'(0)=h'(0), and f''(0)=h''(0)

check your answer by graphing both f and h on www,desmos.com and zoom in around x=0. Explain what you notice.

Answer #1

Use a system of linear equations to find the quadratic
function
f(x) = ax2 + bx + c
that satisfies the given conditions. Solve the system using
matrices.
f(1) = 3, f(2) = 12, f(3) = 25
f(x) =

quadratic function is a function of the form
y=ax2+bx+c where a, b, and c are constants. Given any 3
points in the plane, there is exactly one quadratic function whose
graph contains these points.
Find the quadratic function whose graph contains the points (5,
45), (−3, 5), and (0, 5).
Enter the equation below.

About convex function:
(1) Please show that f(x) = ax2 + bx + c is a convex
function if and only if a ≥ 0.
(2) Please show that f(x) = 1/2·xTQx+aTx
is a convex function if and only if Q is positive
semi-definite.

Find the values of a and b that make
f continuous everywhere.
f(x) =
x2 − 4
x − 2
if x < 2
ax2 − bx + 3
if 2 ≤ x < 3
2x − a + b
if x ≥ 3

Find the quadratic function that is the best fit for f(x)
defined by the table below. x 0 2 4 6 8 10 f(x) 0 401 1598 3602
6391 9990 The quadratic function is y equals = nothing . (Type an
equation using x as the variable. Round to two decimal places as
needed.)

Find the 4th order polynomial that best fits, in a square error
sense, ln(x) on the interval [1,2]. (In other words, use Legendre
polynomials.) Please explain steps and include a plot of the
solution.

1) find a cubic polynomial with only one root
f(x)=ax^3+bx^2+cx +d such that it had a two cycle using Newton’s
method where N(0)=2 and N(2)=0
2) the function G(x)=x^2+k for k>0 must ha e a two cycle
for Newton’s method (why)? Find the two cycle

Find the values of a function f(x) if
f(x) = 2x + 5, for
f(2), f(4),
f(k), and f(x2 +
2)
The difference quotient of a function is given by:
limh0f(x)
fx+h-f(x)h . Find the
difference quotient of, f(x) = 2x + 3 and f(x) = x2 +
2
a. Prove that h(x) and k(x) are inverses of each other when
h(x) =x+213 and k(x) = 3x + 21

Find the Maclaurin polynomial (c = 0) of degree n = 6 for f(x) =
cos(2x). Use a calculator to compare the polynomial evaluated at
π/8 and cos(2π/8)

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

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 10 minutes ago

asked 21 minutes ago

asked 36 minutes ago

asked 44 minutes ago

asked 45 minutes ago

asked 48 minutes ago

asked 48 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago