f(x) =

Step-by-step explanation:

Which polynomial function has x intercepts -1,0, and 2 and passes through the point (1,-6)?

There are 3 distinct and real roots given in the question, which means that the function must be a third degree polynomial. The roots are -1, 0, and 2. This means that f(x) = 0 at these points. The general form of the cubic equation is given by:

f(x) = ax^3 + bx^2 + cx + d; where a, b, c, and d are arbitrary constants.

From the given data:

f(-1)=0 implies a*(-1)^3 + b*(-1)^2 + c(-1) + d = -a + b - c + d = 0. (Equation 1).

f(0)=0 implies a*(0)^3 + b*(0)^2 + c(0) + d = 0a + 0b + 0c + d = 0. (Equation 2).

f(2)=0 implies a*(2)^3 + b*(2)^2 + c(2) + d = 8a + 4b + 2c + d = 0. (Equation 3).

f(1)=0 implies a*(1)^3 + b*(1)^2 + c(1) + d = a + b + c + d = -6. (Equation 4).

Equation 2 shows that d = 0. So rest of the equations become:

-a + b - c = 0;

8a + 4b + 2c = 0; (Divide 2 on both sides of the equation to simplify).

a + b + c = -6

This system of equation can be solved using the Gaussian Elimination Method. Converting the system into the augmented matrix form:

•111|-6

•-11-1|0

•421|0

Adding row 1 into row 3:

•111|-6

•020|-6

•421|0

Dividing row 2 with 2 and multiplying row 1 with -4 and add it into row 3:

•11 1|-6

•01 0|-3

•0-2-3|24

Multiplying row 2 with 2 and add it into row 3:

•11 1|-6

•01 0|-3

•00-3|18

It can be seen that when this updated augmented matrix is converted into a system, it comes out to be:

•a + b + c = -6

•b = -3

•-3c = 18 (This implies that c = -6.)

Put c = -6 and b = -3 in equation 1:

•a + (-3) + (-6) = -6

•a = -6 + 3 + 6

•a = 3.

So f(x) = (All conditions are being satisfied)!!!

It is a positive linear association. Hope this helps!...Read More

3 more answers

answer: i think it's a step-by-step explanation:...Read More

1 more answers

h= 12 inchesstep-by-step explanation:...Read More

2 more answers

1. If I remember from class correctly, your monthly expenses should be about 20% of your net income, so the answer would be D. Although, adding up the expenses would work as well.2...Read More

1 more answers

step-by-step explanation: f(x)=2x^2 -1 translation is a function transformation that transform the function in a way of translating. by translating the function its graph is...Read More

2 more answers

fahrenheitstep-by-step explanation: fahrenheit is more precise than celsius. the ambient temperature on most of the inhabited world ranges from -20 degrees fahrenheit to 110 degree...Read More

1 more answers

47.28 or 47.2857143step-by-step explanation: you just divide 331 by 7 and you get that answer. ( i think so tho)...Read More

2 more answers

60.9774step-by-step explanation: because when you add 47.6 plus 7.32 equals 54.92 and when you add .0574 + 6= 6.0574and when you add 54.92 and 6.0574 you get the answer of 60.9774...Read More

1 more answers

- NEED ANSWERS ASAP: Sphere A has a radius twice sphere B and sphere B h...
- Jasmine earns $36 for 4 hours of baby-sitting. She charges a constant...
- Please help!! I literally can’t fail this...
- The number of flowers, f, that a gardener can plant along a border of...
- Think that I borrowed $1000 from a person and $500 from another person...
- Janice is creating a scrapbook page with vertices (2, 1), (7, 1), (7,...
- Find the vertex of the graph of the quadratic function and determine w...
- The circle (x + 2)2 + (y - 5)2 = 9 is shifted 3 units up and 2 units t...
- Which is equivalent to (4xy – 3z)^2, and what type of special product...
- The Palace of Peace and Accord in Astana, Kazakhstan, was built in 200...