How do you complete the square for $$x^2 + bx$$ ?

To complete the square, take half of $$b$$ , square it, and add it to both sides of the equation.

What must be added to $$x^2 - 4x$$ to make it a perfect square trinomial?

You must add 4 to make it a perfect square trinomial: $$x^2 - 4x + 4 = (x - 2)^2$$ .

Solve $$x^2 + 9x + 9 = 0$$ by completing the square.

$$x = \frac{-9 \text{±} \text{√}(45)}{2}$$ .

Solve $$x^2 - 8x - 14 = 0$$ by completing the square.

$$x = ig\{\text{±}\text{√}(30) + 4\}$$ .

Solve $$x^2 - 4x - 20 = 0$$ by completing the square.

$$x = ig\text{±}2\text{√}(6) + 2$$ .

What is the first step in completing the square for $$x^2 + 6x = 5$$ ?

Rearrange to $$x^2 + 6x - 5 = 0$$ and then add 9 to both sides.

What is the discriminant in a quadratic equation?

The discriminant is the part of the quadratic formula under the square root: $$b^2 - 4ac$$ . It determines the nature of the roots.

What does a positive discriminant indicate?

A positive discriminant indicates that the quadratic equation has two distinct real roots.

What does a zero discriminant indicate?

A zero discriminant indicates that the quadratic equation has exactly one real root (a repeated root).

What does a negative discriminant indicate?

A negative discriminant indicates that the quadratic equation has no real roots, only complex roots.

Solving Quadratic Equations by Completing the Square Flashcards

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15 questions

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1.

FLASHCARD QUESTION

Front

What is a quadratic equation?

Back

2.

FLASHCARD QUESTION

Front

What does it mean to complete 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.

Tags

CCSS.HSA-REI.B.4B

3.

FLASHCARD QUESTION

Front

What is a perfect square trinomial?

Back

Tags

CCSS.HSA.APR.C.4

4.

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSA-REI.B.4B

5.

FLASHCARD QUESTION

Front

What is the formula for solving a quadratic equation by completing the square?

Back

Tags

CCSS.HSA-REI.B.4B

6.

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSA-REI.B.4B

7.

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSA-REI.B.4B

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