MASTER writing a quadratic in vertex form by completing the square to identify the vertex

The video tutorial explains how to identify the vertex of a quadratic equation by converting it from standard form to vertex form using the method of completing the square. The instructor provides a detailed explanation of the process, including the importance of having the coefficient A equal to 1, and demonstrates the method through several examples with different values of A. The tutorial also covers the handling of fractions and negative coefficients, ensuring a comprehensive understanding of the technique.

What is the vertex form of a quadratic equation?

• a * (x - h)^2 + k

• ax^2 + bx

• a(x - h)(x - k)

• ax^2 + bx + c

Why is completing the square useful in algebra?

• It simplifies linear equations.

• It helps in converting quadratic equations to vertex form.

• It is used to solve cubic equations.

• It is a method to find the roots of linear equations.

What is the first step in completing the square when a=1?

• Subtract the linear term from both sides.

• Multiply the equation by 2.

• Add the constant term to both sides.

• Divide the linear coefficient by 2 and square it.

When completing the square, what do you do after adding and subtracting the same number?

• Divide the equation by the added number.

• Multiply the entire equation by the added number.

• Factor the trinomial into a binomial squared.

• Subtract the added number from the constant term.

How do you handle completing the square when the coefficient of x^2 is negative?

• Add the negative sign to the constant term.

• Ignore the negative sign.

• Factor out the negative sign from the quadratic and linear terms.

• Multiply the entire equation by -1.

What should you do if the coefficient of x^2 is not 1 when completing the square?

• Add 1 to the equation.

• Factor out the coefficient from the quadratic and linear terms.

• Subtract the coefficient from the constant term.

• Multiply the equation by the coefficient.

In the context of completing the square, what is a perfect square trinomial?

• A trinomial that can be factored into two identical binomials.

• A trinomial with no real roots.

• A trinomial that cannot be factored.

• A trinomial with a constant term of zero.

What is the vertex of the equation after completing the square: x^2 + 2x - 3?

• (-1, -4)

• (1, 3)

• (0, -3)

• (-2, 1)

How do you convert a whole number to a fraction when dealing with fractions in completing the square?

• Divide the whole number by the numerator of the fraction.

• Subtract the whole number from the fraction.

• Multiply the whole number by the denominator of the fraction.

• Add the whole number to the fraction.

What is the final step in completing the square to find the vertex form?

• Add the constant term to both sides.

• Rewrite the equation as a binomial squared.

• Multiply the equation by the coefficient of x.

• Divide the equation by the coefficient of x^2.