Solving Parabola Equations

The video tutorial explains how to solve a system of equations to find the coefficients A, B, and C for a quadratic equation. It begins by setting up three equations using given points, then simplifies and eliminates variables to solve the system. The process involves subtracting and adding equations to eliminate variables, ultimately finding the values of A, B, and C. The final equation of the parabola is presented, and the video concludes with a channel promotion.

What is the first step in solving for the coefficients a, b, and c in a parabola equation?

• Calculate the slope

• Find the x-intercepts

• Identify the vertex

• Form three equations using given points

How many equations are needed to solve for three unknowns in a parabola equation?

• Four

• Three

• Two

• One

What do you substitute into the general equation to form the three equations?

• Only x-coordinates

• Only y-coordinates

• Both x and y coordinates

• The slope

What is the first equation formed when x=1 and y=3?

• y = a + b + c

• y = a - b + c

• y = a + b - c

• y = a - b - c

What is the simplified form of the equation when x=4 and y=9?

• 16a + 4b + c = 9

• 16a - 4b + c = 9

• 16a + 4b - c = 9

• 16a - 4b - c = 9

Which variable is eliminated first in the system of equations?

• None

• A

• B

• C

What operation is performed to eliminate variable C?

• Addition

• Subtraction

• Multiplication

• Division

After eliminating C, what is the next step?

• Graph the equation

• Find the vertex

• Eliminate B

• Solve for A

What is the value of A after solving the system?

• 3

• 4

• 2

• 1

What is the value of B after back substitution?

• -9

• -7

• -6

• -8