Understanding Parabolas and Systems of Equations

What is the first step in finding the equation of a parabola that passes through three points?

• Calculating the distance between the points

• Finding the midpoint of the points

• Substituting the points into the standard form of a quadratic equation

• Graphing the points on a coordinate plane

Which form of the equation is used to substitute the given points?

• y = mx + b

• y = ax^2 + bx + c

• y = ax + b

• y = a(x - h)^2 + k

What method is suggested for solving the system of equations with three unknowns?

• Graphical method

• Substitution method

• Elimination method

• Matrix method

Why is the elimination method preferred in this scenario?

• It is easier with three equations and three unknowns

• It is faster than substitution

• It requires less calculation

• It provides an exact solution

What is the result of eliminating variable C from the first two equations?

• A new equation with A, B, and C

• A new equation with B and C

• A new equation with A and C

• A new equation with A and B

After finding the value of A, what is the next step?

• Graph the equation

• Substitute A into one of the original equations to find B

• Check the solution with the original points

• Find the value of C

What is the value of A found in the solution?

• 3

• 2

• 1

• 0

How is the value of B determined?

• By substituting A into one of the new equations

• By using the quadratic formula

• By graphing the points

• By trial and error

What is the final step in forming the equation of the parabola?

• Finding the vertex of the parabola

• Checking the solution with the original points

• Graphing the equation

• Substituting A, B, and C back into the standard form

What is the final equation of the parabola?

• y = x^2 + 2x - 5

• y = x^2 - 2x + 5

• y = x^2 + 3x - 5

• y = x^2 - 3x + 5