How do you find the value to complete the square for the expression $$x^2 - 4x$$ ?

Take half of the coefficient of x (which is -4), square it, resulting in 4. Thus, $$x^2 - 4x + 4 = (x - 2)^2$$ .

How do you complete the square for the equation $$2x^2 - 20x + 18 = 0$$ ?

First, divide by 2: $$x^2 - 10x + 9 = 0$$ . Then, complete the square: $$x^2 - 10x + 25 = 16$$ , leading to $$(x - 5)^2 = 16$$ .

What is the first step in completing the square for the equation $$3x^2 + 15 = 18x$$ ?

Rearrange the equation to standard form: $$3x^2 - 18x + 15 = 0$$ , then divide by 3 to simplify.

What do you do with the b value when completing the square?

Divide the b value by 2 and square the result to find the constant needed to complete the square.

What is the completed square form of the expression $$x^2 - 6x$$ ?

The completed square form is $$(x - 3)^2 - 9$$ .

How do you solve the equation $$x^2 - 4x - 5 = 0$$ by completing the square?

Rearrange to $$x^2 - 4x = 5$$ , complete the square to get $$(x - 2)^2 = 9$$ , then solve for x.

What is the relationship between the roots of a quadratic equation and its graph?

The roots of a quadratic equation correspond to the x-intercepts of its graph, where the parabola intersects the x-axis.

How can completing the square help in graphing a quadratic function?

Completing the square allows you to rewrite the quadratic in vertex form, making it easier to identify the vertex and the direction of the parabola.

What is the effect of the coefficient 'a' in the quadratic equation $$y = ax^2 + bx + c$$ ?

The coefficient 'a' determines the direction of the parabola (upward if a > 0, downward if a

Completing the square Flashcards

Student preview

15 questions

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1.

FLASHCARD QUESTION

Front

What is the process of completing the square?

Back

Completing the square is a method used to convert a quadratic equation into a perfect square trinomial, making it easier to solve or analyze.

Tags

CCSS.HSA-REI.B.4B

2.

FLASHCARD QUESTION

Front

What is the standard form of a quadratic equation?

Back

3.

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSA-REI.B.4B

4.

FLASHCARD QUESTION

Front

What is the vertex form of a quadratic equation?

Back

5.

FLASHCARD QUESTION

Front

How do you derive the vertex from the standard form of a quadratic equation?

Back

6.

FLASHCARD QUESTION

Front

What does the discriminant of a quadratic equation tell you?

Back

Tags

CCSS.HSA-REI.B.4B

7.

FLASHCARD QUESTION

Front

What is the significance of the plus or minus symbol (±) in solving quadratic equations?

Back

The ± symbol indicates that there are two possible solutions when taking the square root of both sides of an equation.

Tags

CCSS.HSA-REI.B.4B

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