find a quadratic function that fits the set of data points.
(1,4), (-1.6), (-2,16)
what did i do wrong, i got -2x^2-x+7
his looks familiar, but I can't find it. Here it is:
plug in the x,y values in the equation
ax^2 + bx + c = y
a + b + c = 4
a - b + c = 6
4a - 2b + c = 16
a = 3
b = -1
c = 2
y = 3x^2 - x + 2
Don't know where you took a wrong turn.
To find a quadratic function that fits a set of data points, you need to solve a system of equations using the given points. Let's go through the process step by step:
1. Start by assuming that the quadratic function you are trying to find is in the form f(x) = ax^2 + bx + c.
2. Next, substitute the x and y coordinate values from each given point into the equation. This will give you a system of three equations with three unknowns (a, b, and c) in terms of the given points:
For the point (1, 4):
4 = a(1)^2 + b(1) + c
For the point (-1, 6):
6 = a(-1)^2 + b(-1) + c
For the point (-2, 16):
16 = a(-2)^2 + b(-2) + c
3. Simplify each equation:
Equation 1: 4 = a + b + c
Equation 2: 6 = a - b + c
Equation 3: 16 = 4a - 2b + c
4. You now have a system of three linear equations. Solve this system to find the values of a, b, and c.
One possible way to solve this type of system is by using a matrix:
[1 1 1 | 4 ]
[1 -1 1 | 6 ]
[4 -2 1 | 16 ]
Reduce the matrix to row-echelon form or use the method of your choice to solve for a, b, and c. The result should be:
a = 2
b = -5
c = 7
5. Now that you have the values of a, b, and c, you can write the quadratic function:
f(x) = 2x^2 - 5x + 7
So, the quadratic function that fits the given set of data points is f(x) = 2x^2 - 5x + 7.
It seems that you made a small error in your calculation, resulting in a slightly different quadratic function.