Standard Form of Quadratic Equations

The video tutorial explains how to rewrite a quadratic equation in standard form, which is ax^2 + bx + c = 0. The process involves moving all terms to the left-hand side and arranging them in descending order of exponents. The tutorial demonstrates this by transforming the equation 6x^2 + 3 = 2x - 6 into standard form, resulting in 6x^2 - 2x + 9 = 0. It further identifies the coefficients a, b, and c as 6, -2, and 9, respectively.

What is the first step in rewriting the equation 6x^2 + 3 = 2x - 6 in standard form?

• Divide both sides by 3

• Multiply both sides by 2

• Subtract 2x from both sides

• Add 6 to both sides

In the standard form of a quadratic equation, what is the order of terms?

• x squared term, x term, constant

• x term, x squared term, constant

• Constant, x term, x squared term

• x squared term, constant, x term

After subtracting 2x from both sides, what is the next step to simplify the equation?

• Add 3 to both sides

• Subtract 3 from both sides

• Subtract 6 from both sides

• Add 6 to both sides

What does the equation become after adding 6 to both sides?

• 6x^2 + 2x + 3 = 0

• 6x^2 - 2x + 3 = 0

• 6x^2 + 2x + 9 = 0

• 6x^2 - 2x + 9 = 0

Why is it important to write the terms in descending order of exponents?

• To make the equation easier to solve

• To ensure the equation is in standard form

• To simplify the calculation of roots

• To reduce the number of terms

What is the value of 'a' in the standard form of the equation?

• 3

• 6

• 2

• 9

What is the value of 'b' in the standard form of the equation?

• 2

• -2

• 6

• -6

What is the value of 'c' in the standard form of the equation?

• 3

• 6

• 9

• 0

Which of the following is NOT a characteristic of the standard form of a quadratic equation?

• The constant term is always positive

• The equation equals zero

• The x term is squared

• All terms are on one side of the equation