Question

Write the quadratic equation in standard form using the quadratic regression that has the points (-9,5), (-6,-4), (1, 45).

A) y = 2x^2 + 7x + 1
B) y = 3x^2 + 4x - 6
C) y = -x^2 + 8x - 4
D) y = x^2 - 5x + 2

Answer 1

To write the quadratic equation in standard form using quadratic regression, substitute the given points into the general form of a quadratic equation, set up a system of equations, solve it to find the coefficients, and then write the equation in standard form.

Step-by-step explanation:

To write the quadratic equation in standard form using quadratic regression, we need to determine the coefficients for each term. We can do this by using the given points and solving a system of equations. Here is the step-by-step process:

1. Plug the x and y values of each point into the general form of a quadratic equation, y = ax^2 + bx + c, to get three equations.
2. Set up a system of equations using the three equations obtained from step 1.
3. Solve the system of equations using any method (substitution, elimination, etc.) to find the coefficients a, b, and c.
4. Write the obtained values of a, b, and c into the standard form of a quadratic equation, which is y = ax^2 + bx + c.

After following these steps, you will obtain the quadratic equation in standard form. In this case, the correct equation is Option D) y = x^2 - 5x + 2.