Podcast
Questions and Answers
Which technique can be used to rewrite a quadratic expression as a perfect square trinomial?
Which technique can be used to rewrite a quadratic expression as a perfect square trinomial?
- Factoring
- Completing the square (correct)
- Using the square root property
- Multiplying by the conjugate
Which step is involved in solving quadratic equations by completing the square?
Which step is involved in solving quadratic equations by completing the square?
- Rewriting the equation in the form x2 + bx = c
- Solving the resulting equation using the square root property
- Adding the term needed to complete the square
- Factoring the perfect square trinomial (correct)
What is the term needed to complete the square if the quadratic expression is x^2 + 6x?
What is the term needed to complete the square if the quadratic expression is x^2 + 6x?
- 12
- 18
- 36
- 9 (correct)
When completing the square, what is the square of half the coefficient of the linear x?
When completing the square, what is the square of half the coefficient of the linear x?
What property is used to solve the resulting equation after completing the square?
What property is used to solve the resulting equation after completing the square?
Which technique can be used to rewrite a quadratic expression as a perfect square trinomial?
Which technique can be used to rewrite a quadratic expression as a perfect square trinomial?
What is the term needed to complete the square if the quadratic expression is $x^2 + 6x$?
What is the term needed to complete the square if the quadratic expression is $x^2 + 6x$?
Which step is involved in solving quadratic equations by completing the square?
Which step is involved in solving quadratic equations by completing the square?
What property is used to solve the resulting equation after completing the square?
What property is used to solve the resulting equation after completing the square?
When completing the square, what is the square of half the coefficient of the linear term?
When completing the square, what is the square of half the coefficient of the linear term?
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Study Notes
Completing the Square
- To rewrite a quadratic expression as a perfect square trinomial, the technique of completing the square is used.
Solving Quadratic Equations
- To solve quadratic equations by completing the square, the step involved is adding a value to both sides of the equation to make one side a perfect square trinomial.
Completing the Square Formula
- To complete the square, the term needed is $(b/2)^2$, where $b$ is the coefficient of the linear term $x$.
- For the quadratic expression $x^2 + 6x$, the term needed to complete the square is $(6/2)^2 = 3^2 = 9$.
Solving the Resulting Equation
- After completing the square, the property used to solve the resulting equation is the difference of squares property, which states that $a^2 - b^2 = (a + b)(a - b)$.
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