Solving Equations with Variables

The video tutorial explains how to derive the equation of a parabola in its general form using three given points. It starts by introducing the general form of a parabola equation and then sets up three equations using the given points. The tutorial demonstrates solving for the constant C first, followed by using elimination to solve for variables A and B. Finally, it combines the results to form the complete equation of the parabola.

What is the general form of a parabola equation?

• y = ax^3 + bx^2 + c

• y = ax^2 + b

• y = ax^2 + bx + c

• y = ax + b

How many equations are needed to solve for three variables?

• Two

• One

• Four

• Three

What value is determined when x is 0 in the equation y = ax^2 + bx + c?

• a

• b

• c

• x

What is the value of C when y is 11 and x is 0?

• 11

• 5

• 0

• 3

What is the simplified form of the equation when y is 5 and x is 1?

• a + c = 5

• a + b = 5

• a + b + c = 5

• b + c = 5

What is the equation when y is 3 and x is 2?

• a + 2b + c = 3

• 2a + b + c = 3

• a + b + c = 3

• 4a + 2b + c = 3

What is the result of subtracting 11 from both sides of the equation a + b + c = 5?

• a + b = -6

• a + b = 6

• a + b = -5

• a + b = 5

What is the result of subtracting 11 from both sides of the equation 4a + 2b + c = 3?

• 4a + 2b = 8

• 4a + 2b = -3

• 4a + 2b = -8

• 4a + 2b = 3

What is the value of a after solving the equations?

• 2

• 1

• 3

• 4

What operation is performed to eliminate b from the equations?

• Addition

• Subtraction

• Division

• Multiplication