Determine the domain and range of a quadratic by rewriting in vertex form

The video tutorial explains the conversion of quadratic equations from standard form to vertex form. It covers the steps involved in creating perfect square trinomials and discusses the properties of equality in equations. The tutorial also analyzes the vertex, axis of symmetry, domain, and range of quadratic graphs.

What is the standard form of a quadratic equation?

• ax^2 + bx + c

• a(x - h)^2 + k

• ax + b

• a(x + h)^2 - k

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

• Factor the quadratic term

• Group the quadratic and linear terms

• Solve for x

• Add and subtract the same number

How do you create a perfect square trinomial?

• Subtract the linear term from the quadratic term

• Add the constant term to the quadratic term

• Divide the linear coefficient by 2 and square it

• Multiply the quadratic term by 2

Why is it important to add and subtract the same value when converting to vertex form?

• To change the equation's value

• To maintain equivalent equations

• To simplify the equation

• To solve for x

What is the vertex form of a quadratic equation?

• a(x + h)^2 - k

• ax + b

• a(x - h)^2 + k

• ax^2 + bx + c

What happens to the graph of a quadratic when the vertex is moved?

• It rotates around the origin

• It becomes a straight line

• It shifts horizontally and vertically

• It remains unchanged

What is the range of a quadratic function with a vertex at (-5, -22)?

• (-∞, ∞)

• (-22, ∞)

• (0, ∞)

• (-∞, 0)