Final answer:
To write a quadratic equation from three points, create a system of equations using those points and solve for the quadratic coefficients. Alternatively, for a known quadratic equation, use the quadratic formula to find solutions by substituting the values for a, b, and c.
Step-by-step explanation:
To write a quadratic equation given three points, you can use those points to set up a system of equations and solve for the coefficients a, b, c of the quadratic equation in the form ax² + bx + c = y.
Let's consider the example with points (294.5, 61), (364, 70), and (605.5, 88.5). Using these points, we would set up three equations:
1. 294.5² * a + 294.5 * b + c = 61,
2. 364² * a + 364 * b + c = 70,
3. 605.5² * a + 605.5 * b + c = 88.5.
Solve this system of equations to find a, b, and c. Once these values are obtained, plug them back into the quadratic equation ax² + bx + c = y to get your required equation. This process can also be completed using a calculator with the capability to do regression analysis or solve systems of equations.If the quadratic equation is known, for example ax² + bx + c = 0 where a = A quadratic equation can be written in the form ax² + bx + c = 0, where a, b, and c are constants. To find a quadratic equation given three points, you can substitute the x and y values of each point into the general form of the equation and solve for the variables. This will give you a system of three equations that can be solved simultaneously to find the values of a, b, and c
For example, let's say the three points are (x1, y1), (x2, y2), and (x3, y3). Substituting each point into the equation gives youYou can then solve these equations simultaneously to find the values of a, b, and c. Once you have these values, you can write the quadratic equation in the form ax² + bx + c = 0.1.00, b = 10.0, and c = -200, you can find the solutions using the quadratic formula, which states that the solutions for x can be found using the formula x = (-b ± √(b² - 4ac)) / (2a). Substitute the known values of a, b, and c to calculate the solutions for x.