To create a quadratic formula, we must find the coefficients a, b, and c in the general quadratic equation y = ax^2 + bx + c by substituting the given x and y values into the equation. This will result in a system of equations that can be solved to find a, b, and c.
Using the given x and y values:
1. Substitute the first point (x=10, y=6.36) into the equation:
6.36 = a(10)^2 + b(10) + c
6.36 = 100a + 10b + c
2. Substitute the second point (x=20, y=11.38) into the equation:
11.38 = a(20)^2 + b(20) + c
11.38 = 400a + 20b + c
3. Substitute the third point (x=25, y=13.98) into the equation:
13.98 = a(25)^2 + b(25) + c
13.98 = 625a + 25b + c
Solving the system of equations formed by these three equations will give us the values of a, b, and c. Once we have found these values, we can write the quadratic formula:
y = ax^2 + bx + c
Substitute the values of a, b, and c into the equation to get the final quadratic formula.
x-10,20,25,30,35,65,75,80,85,95
y-6.36,11.38,13.98,16.23,17.01,18,98,18.91,19.04,15.22,11.39
create a quadratic formula using x and y values
1 answer
1 answer