Identify the vertex, domain and range from a quadratic by completing the square

The video tutorial explains the process of converting quadratic equations from standard form to vertex form. It highlights the importance of understanding binomial squares and perfect square trinomials. The instructor provides a step-by-step guide and demonstrates the process with an example problem, emphasizing key concepts like vertex identification, axis of symmetry, domain, and range.

What is the main difference between the standard form and vertex form of a quadratic equation?

• The standard form does not include any constants.

• The vertex form includes a binomial squared.

• The vertex form is always linear.

• The standard form has a higher degree.

How do you create a binomial squared?

• By multiplying two linear terms.

• By factoring a perfect square trinomial.

• By adding a constant to the equation.

• By dividing the equation by a constant.

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

• Factor the quadratic term.

• Group the quadratic and linear terms.

• Subtract a constant from the equation.

• Add a constant to the equation.

Why is it important to add and subtract the same value when completing the square?

• To maintain the balance of the equation.

• To change the equation's degree.

• To eliminate the linear term.

• To simplify the equation.

What is the vertex of the function f(x) = (x - 3)^2 - 7?

• (3, 7)

• (-3, 7)

• (-3, -7)

• (3, -7)

What is the axis of symmetry for the function f(x) = (x - 3)^2 - 7?

• x = -3

• x = 3

• x = 7

• x = -7

What is the range of the function f(x) = (x - 3)^2 - 7?

• [-7, ∞)

• (-∞, 7]

• (-7, ∞)

• (-∞, -7]