Solving Quadratic Equations and Functions

This video tutorial explains how to solve a quadratic equation by completing the square. It assumes prior knowledge of the basic steps involved. The process includes moving the constant term, making the leading coefficient one, creating a perfect square trinomial, and factoring it to solve for x. The video concludes with the final solution, highlighting the presence of two real irrational solutions.

What is the first step in solving a quadratic equation by completing the square?

• Move the constant term to the right side of the equation.

• Multiply all terms by the leading coefficient.

• Factor the quadratic equation.

• Add a constant to both sides.

Why do we divide every term by the leading coefficient in the equation?

• To eliminate fractions from the equation.

• To ensure the leading coefficient is one.

• To simplify the constant term.

• To make the equation easier to solve.

What is the formula used to determine the constant needed for a perfect square trinomial?

• B squared times 2

• B times 2 squared

• B squared divided by 2

• B divided by 2 squared

What is the purpose of adding the same constant to both sides of the equation?

• To balance the equation.

• To simplify the equation.

• To factor the equation.

• To eliminate the constant term.

How do you solve for x after factoring the trinomial?

• By dividing both sides by the constant.

• By adding the constant to both sides.

• By taking the square root of both sides.

• By multiplying both sides by the constant.

Why is it important to have a common denominator when adding fractions on the right side?

• To eliminate the constant term.

• To simplify the equation.

• To ensure the equation is balanced.

• To make the equation easier to factor.

What must be done to obtain all solutions when taking the square root of both sides?

• Divide by the constant term.

• Multiply by the leading coefficient.

• Include a plus or minus sign.

• Add a constant to both sides.

What is the final form of the solution when expressed as a single fraction?

• X equals a numerator of 7 plus or minus square root 73 all over 6.

• X equals a numerator of 7 plus square root 73 all over 6.

• X equals a numerator of 7 minus square root 73 all over 6.

• X equals a numerator of 7 plus or minus square root 73 all over 3.

What type of solutions are obtained when the square root of 73 is involved?

• Two imaginary solutions.

• One real and one imaginary solution.

• Two real irrational solutions.

• Two real rational solutions.

What does the expression X equals 7 plus or minus square root 73 all over 6 represent?

• A single solution.

• Two solutions.

• No solution.

• An imaginary solution.