Question

Create a system of equations and use algebra to write a quadratic equation for each set of three

points that lie on a parabola.
1. (-3, 12), (0, 9), (3, 24).

Answer 1

To find the quadratic equation for the parabola passing through the points (-3, 12), (0, 9), and (3, 24), we substitute these points into the standard quadratic form, create a system of linear equations, and solve for a, b, and c to construct the quadratic equation.

Step-by-step explanation:

To create a quadratic equation from the given points (-3, 12), (0, 9), and (3, 24) that lie on a parabola, we use the standard form of a quadratic equation, which is y = ax² + bx + c. For each of these points, we substitute the x and y values into the equation to produce a system of equations:

• Point (-3, 12): 12 = a(-3)² + b(-3) + c
• Point (0, 9): 9 = a(0)² + b(0) + c
• Point (3, 24): 24 = a(3)² + b(3) + c

Solving this system of equations, we start with the equation from the point (0, 9), which immediately gives us c = 9. Substituting this value into the other equations, we get:

• 12 = 9a - 3b + 9
• 24 = 9a + 3b + 9

Solving this system of linear equations simultaneously gives us the values of a and b. After finding the values of a, b, and c, we can construct the quadratic equation of the parabola.