Quadratic Functions and Equations

This video tutorial explains how to find the equation of a quadratic function in standard form using given points. It covers the process of determining the coefficients A, B, and C by solving systems of equations. The tutorial includes example problems to illustrate the method and concludes with additional resources for further learning.

What is the standard form of a quadratic equation?

• y = ax^3 + bx^2 + c

• y = ax^2 + b

• y = ax^2 + bx + c

• y = ax + b

If a quadratic function passes through the point (0, 7), what is the value of c?

• 0

• Cannot be determined

• 7

• 1

Which method can be used to solve a system of equations for a quadratic function?

• Graphing

• Both Substitution and Elimination

• Substitution

• Elimination

What is the first step in solving for a and b using elimination?

• Multiply one equation by -1

• Add the equations

• Subtract the equations

• Divide the equations

What is the value of a if 6 = 2a?

• 4

• 3

• 2

• 1

How many equations are needed to solve for three variables in a quadratic function?

• Three

• Two

• One

• Four

What is the result of adding the equations -3 = a - b - c and 11 = 9a + 3b + c?

• 8 = 9a + 3b

• 8 = 9a + 2b

• 8 = 8a + 2b

• 8 = 8a + 3b

What is the value of b if 2 = 3a + b and a = 2?

• 2

• 0

• 4

• -4

What is the final equation of the quadratic function if a = 2, b = -4, and c = 5?

• y = 2x^2 - 4x + 5

• y = 2x^2 + 4x - 5

• y = 2x^2 + 4x + 5

• y = 2x^2 - 4x - 5

What is the importance of checking your work when solving for coefficients?

• To ensure the solution is correct

• To find new solutions

• To make the process faster

• To avoid using elimination