Tuesday

July 22, 2014

July 22, 2014

Posted by **Lisa** on Tuesday, October 23, 2007 at 4:26pm.

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 x-axis at -4, 0, and 1; lies above the x-axis between -4 and 0; lies below the x-axis between 0 and 1.

#2.Touches the x-axis at 0 and crosses the x-axis at 4; lies below the x-axis between 0 and 4

- Writing equation of a polynomial function -
**Reiny**, Tuesday, October 23, 2007 at 5:11pmfor #1

x-intercepts 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)x-0)(x-1)

or

f(x) = x(x-1)(x+4) . You can expand it or leave it as is

for #2

if a graph "touches" the x-axis then there must have been a double root, such as (x-2)(x-2)

so this one clearly must have been

f(x) = (x-0)(x-0)(x-4)

= x^2(x-4)

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

**Related Questions**

Polynomial Function - Could you help me with the following problem, I dont ...

Algebra help! - I dont understand my problems that I am suppose to do. please ...

Writing polynomial functions - How to write a polynomial function with the ...

Polynomial Fucntion Problem - Could you help me with the following problem, I ...

Algebra - please help me with this question and check my answers. Solve the ...

Math - polynomial function - Write a polynomial function with integral ...

algebra - HELP!!!!!!!!!!!!! write equation of a polynomial function with the ...

pre cal - Use synthetic division to show that x is a solution of the third-...

Math:Polynomial Functions - h(x) = -7x I was thinking that this was not a ...

Math - Use synthetic division to show that x is a solution of the third-degree ...