Quadratic Equations and Functions

This video tutorial explains how to find the equation of a quadratic function from a graph. It covers using the vertex form when the vertex is known and converting it to standard form. Additionally, it demonstrates finding the quadratic equation using three points when the vertex is unknown, employing systems of equations to solve for coefficients.

What is the vertex form of a quadratic equation?

• y = a(x - h)^2 + k

• y = ax^2 + bx + c

• y = a(x + h)^2 - k

• y = ax^2 - bx + c

If the vertex of a quadratic function is (3, -4), what are the values of h and k in the vertex form?

• h = 4, k = 3

• h = -3, k = 4

• h = 3, k = -4

• h = -4, k = 3

What is the first step in converting the vertex form to the standard form of a quadratic equation?

• Combine like terms

• Add the constant term

• Distribute the leading coefficient

• Expand the squared term

When given three points on a quadratic graph, which form of the equation should be used if the vertex is unknown?

• Factored form

• Standard form

• Linear form

• Vertex form

What is the value of c in the standard form equation if the y-intercept is -2?

• c = 0

• c = -2

• c = 2

• c = -1

How many points are needed to determine a quadratic equation in standard form?

• Four

• Two

• One

• Three

What method is used to solve for the coefficients a, b, and c when given three points?

• Substitution

• Factoring

• Graphing

• Elimination

If a system of equations results in 9 = 3a, what is the value of a?

• a = 4

• a = 2

• a = 1

• a = 3

What is the next step after finding the value of a in a system of equations?

• Check the solution

• Graph the equation

• Solve for c

• Solve for b

What is the standard form of a quadratic equation?

• y = a(x + h)^2 - k

• y = ax^2 + bx + c

• y = a(x - h)^2 + k

• y = ax^2 - bx + c