How do you solve the equation $$x^2 + 12x = 5$$ using completing the square?

Rearrange to $$x^2 + 12x - 5 = 0$$ , complete the square to find $$x = -6 \\pm \\sqrt{41}$$ .

How do you solve the equation $$n^2 - 2n - 3 = 0$$ ?

Factor to find $$n = 3$$ and $$n = -1$$ .

What is the significance of the discriminant in a quadratic equation?

It determines the nature of the roots: positive for two real roots, zero for one real root, and negative for no real roots.

What is the formula for the vertex of a parabola given by a quadratic equation?

The vertex is at $$(h, k)$$ where $$h = -\frac{b}{2a}$$ and $$k = f(h)$$ .

How do you convert a standard form quadratic equation to vertex form?

Complete the square on the quadratic expression.

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

The coefficients determine the shape, direction, and position of the parabola.

What is the general form of a quadratic equation?

$$ax^2 + bx + c = 0$$ where a, b, and c are constants.

How can you check your solution after completing the square?

Substitute the solution back into the original equation to verify.

1st Flashcard 6 review completing the square Flashcards

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15 questions

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1.

FLASHCARD QUESTION

Front

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

Back

Move the constant term to the other side of the equation.

2.

FLASHCARD QUESTION

Front

How do you find the value to complete the square for the term 'bx'?

Back

Divide 'b' by 2 and square the result.

3.

FLASHCARD QUESTION

Front

Back

4.

FLASHCARD QUESTION

Front

What does the vertex form of a quadratic equation look like?

Back

5.

FLASHCARD QUESTION

Front

Back

6.

FLASHCARD QUESTION

Front

Back

7.

FLASHCARD QUESTION

Front

Back

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