Question

Use a system of linear equations to find the quadratic function

f(x) = ax^{2} + bx + c

that satisfies the given conditions. Solve the system using matrices.

f(1) = 3, f(2) = 12, f(3) = 25

f(x) =

Answer #1

Use a system of equations to find the cubic function
f(x) = ax3 + bx2 + cx + d
that satisfies the equations. Solve the system using
matrices.
f(−1) = 10
f(1) = 8
f(2) = 34
f(3) = 94

find the values of a,b and c for the quadratic polynomial f(x)=
ax2+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.

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.

Suppose that you were to try to find a parabola y =
ax2 + bx + c that passes through the
(x, y) pairs (-5,12), (-4,-2), and (-2,5). To
obtain the coefficients a, b, and c you
would try to solve a system of linear equations whose augmented
matrix is which?

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.

How do you use Gaussian Elimination to work this one out? Solve
a system of linear equations to find the quadratic polynomial y =
ax^2 + bx + c whose graph passes through the three points (x1, y1)
= (1, 4), (x2, y2) = (2, 2) and (x3, y3) = (3, −2).

Find the a, b, c so that y =
ax2 + bx + c goes through the given points.
a. (1, 3), (2, 5), and (3,
1)
b. (-1, -2), (1, -1), and (3,
10)

Find the linear, quadratic and cubic approximations for f(x) =
e^x.

Find the linear, quadratic, and cubic approximations for f(x) =
the square root of (x+1)

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.)

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