Quadratic Equations: Standard to Vertex Form

This video tutorial teaches how to convert quadratic equations from standard form to vertex form using the completing the square method. It covers examples with a leading coefficient of 1 and those with different coefficients. The process involves finding half of the x term's coefficient, squaring it, and adjusting the equation to maintain its value. The tutorial also includes a challenging example with fractional coefficients. Viewers are encouraged to engage with the content by liking, subscribing, and commenting.

What is the first step in converting a quadratic equation from standard form to vertex form when the leading coefficient is 1?

• Find half of the coefficient of the x term and square it.

• Double the coefficient of the x term.

• Subtract the constant term from both sides.

• Find the square root of the constant term.

When completing the square, why do we add and subtract the same number?

• To maintain the equation's value.

• To change the equation's value.

• To eliminate the x term.

• To simplify the equation.

In the vertex form of a quadratic equation, what does the 'h' represent?

• The opposite of the number inside the parentheses.

• The constant term.

• The leading coefficient.

• The square of the x term.

What should be done first when the leading coefficient is not 1?

• Add the constant term to both sides.

• Factor out the leading coefficient from the variable terms.

• Multiply the equation by the leading coefficient.

• Divide the entire equation by the constant term.

How do you maintain the equation's value when the trinomial is multiplied by a factor?

• Add the product of the factor and the added value.

• Add the factor to both sides.

• Subtract the factor from both sides.

• Subtract the product of the factor and the added value.

In the example with a leading coefficient of 5, what is the vertex of the equation?

• (-3, 4)

• (3, 4)

• (-2, -21)

• (2, -21)

What is the initial step when the leading coefficient is negative?

• Add the constant term to both sides.

• Divide the entire equation by the constant term.

• Factor out the negative leading coefficient.

• Multiply the equation by the negative coefficient.

How do you handle fractions when completing the square?

• Multiply them by the leading coefficient.

• Leave them as fractions.

• Ignore them.

• Convert them to decimals.

In the challenging example, what is the vertex of the equation?

• (3/2, -41/4)

• (-3/2, 41/4)

• (3/2, 41/4)

• (-3/2, -41/4)

What should you do if you found the video helpful?

• Give it a thumbs up and subscribe.

• Report it.

• Dislike it.

• Ignore it.