Identify the equivalent expression for the trinomial $$x^2 - 18x + 81$$ .

The equivalent expression is $$ (x - 9)^2 $$ .

Solve the equation by completing the square: $$x^2 + 12x = 5$$ .

The solutions are $$x = 6 \\pm \\sqrt{41}$$ .

When factoring $$x^2 - 4x + 4 = 20$$ , what goes in the blank? $$ (x - __)^2 = 20 $$

The blank is filled with 2, so it becomes $$ (x - 2)^2 = 20 $$ .

Solve the equation by completing the square: $$x^2 + 6x - 4 = 36$$ .

The solutions are $$x = -4 \\pm \\sqrt{7}$$ .

What value of c makes the expression $$x^2 - 14x + c = 0$$ a perfect square trinomial?

The value of c that makes it a perfect square trinomial is c = 49.

What is the standard form of a quadratic equation?

The standard form of a quadratic equation is $$ax^2 + bx + c = 0$$ , where a, b, and c are constants and a ≠ 0.

How do you derive the quadratic formula from completing the square?

Starting from the standard form $$ax^2 + bx + c = 0$$ , divide by a, rearrange, complete the square, and solve for x to derive $$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$ .

What is the discriminant in a quadratic equation?

The discriminant is the part of the quadratic formula under the square root, given by $$b^2 - 4ac$$ . It determines the nature of the roots: if positive, two real roots; if zero, one real root; if negative, two complex roots.

A binomial is a polynomial with two terms, such as $$a + b$$ or $$x^2 - 4$$ .

What does it mean for a quadratic equation to have complex solutions?

A quadratic equation has complex solutions when the discriminant is negative, indicating that the roots cannot be expressed as real numbers.

What is the vertex form of a quadratic function?

The vertex form of a quadratic function is $$y = a(x - h)^2 + k$$ , where (h, k) is the vertex of the parabola.

5.5&5.6 HW Completing the Square and Solving Complex Flashcard

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14 questions

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1.

FLASHCARD QUESTION

Front

What is a perfect square trinomial?

Back

A perfect square trinomial is a quadratic expression that can be expressed as the square of a binomial. It takes the form: (a + b)² = a² + 2ab + b² or (a - b)² = a² - 2ab + b².

2.

FLASHCARD QUESTION

Front

Back

3.

FLASHCARD QUESTION

Front

What is the process of completing the square?

Back

Completing the square is a method used to solve quadratic equations by rewriting the equation in the form of a perfect square trinomial, allowing for easier solutions.

4.

FLASHCARD QUESTION

Front

Back

5.

FLASHCARD QUESTION

Front

Back

6.

FLASHCARD QUESTION

Front

Back

The vertex (h, k) can be found using h = -b/(2a) and k = f(h).

7.

FLASHCARD QUESTION

Front

Back

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