Posted by Lisa on Tuesday, October 23, 2007 at 4:26pm.
Can you help me with the following questions, I don't understand. thanks!
Write the equation of a polynomial function with the given characteristics. Use a leading coefficient of 1 or 1 and make the degree of the function as small as possible.
#1. Crosses the xaxis at 4, 0, and 1; lies above the xaxis between 4 and 0; lies below the xaxis between 0 and 1.
#2.Touches the xaxis at 0 and crosses the xaxis at 4; lies below the xaxis between 0 and 4

Writing equation of a polynomial function  Reiny, Tuesday, October 23, 2007 at 5:11pm
for #1
xintercepts of a function are solutions to the corresponding equation
since there are solutions of 4,0,and 1
the function must have been f(x) = (x+4)x0)(x1)
or
f(x) = x(x1)(x+4) . You can expand it or leave it as is
for #2
if a graph "touches" the xaxis then there must have been a double root, such as (x2)(x2)
so this one clearly must have been
f(x) = (x0)(x0)(x4)
= x^2(x4)
In both cases we need a cubic for 3 roots. If the x^3 is positive, then the cubic "rises" into the first quadrant and "drops" into the third quadrant.
Since this was the case for both functions there would be a +1 understood in front of the factors,
had it been reversed, a 1 in front of the factors would have achieved this
Answer This Question
Related Questions
 Algebra help!  I don't understand my problems that I am suppose to do. please ...
 algebra  HELP!!!!!!!!!!!!! write equation of a polynomial function with the ...
 Math  1. Identify the degree, leading term and leading coefficient of each ...
 Math  Determine whether the following statement makes sense or does not make ...
 Polynomial Function  Could you help me with the following problem, I don't ...
 Math  Write a polynomial function in standard form that has the given zeros and...
 poloynomial function  Write a polynomial function f of least degree that has ...
 algebra 2  Write a polynomial function that has the zeros 2, 2, and 1 and has...
 Precalculus  I'm sorry I'm posting so many questions, I promise this is the ...
 algebra  A cubic polynomial function f(x) has leading coefficient 2 and ...
More Related Questions