5.5&5.6 HW Completing the Square and Solving Complex

5.5&5.6 HW Completing the Square and Solving Complex

Assessment

Flashcard

Mathematics

9th - 12th Grade

Practice Problem

Hard

Created by

Wayground Content

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15 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

How do you find the value of c to make x² - 14x + c a perfect square trinomial?

Back

To find c, take half of the coefficient of x (which is -14), square it: (-14/2)² = 49. Thus, c = 49.

3.

FLASHCARD QUESTION

Front

What is the vertex form of a quadratic function?

Back

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

4.

FLASHCARD QUESTION

Front

How do you complete the square for the equation x² + 12x = 5?

Back

1. Move 5 to the other side: x² + 12x - 5 = 0. 2. Take half of 12, square it: (12/2)² = 36. 3. Add 36 to both sides: x² + 12x + 36 = 41. 4. Factor: (x + 6)² = 41.

5.

FLASHCARD QUESTION

Front

What are the solutions to the equation x² + 12x - 5 = 0 after completing the square?

Back

The solutions are x = -6 ± √41.

6.

FLASHCARD QUESTION

Front

What is the formula for the vertex of a quadratic function in standard form y = ax² + bx + c?

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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