
Solving Quadratics by Completing the Square
Flashcard
•
Mathematics
•
6th - 8th Grade
•
Hard
Wayground Content
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15 questions
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1.
FLASHCARD QUESTION
Front
What is the method of completing the square?
Back
Completing the square is a method used to solve quadratic equations by rewriting the equation in the form (x + p)² = q, making it easier to solve for x.
2.
FLASHCARD QUESTION
Front
What is the standard form of a quadratic equation?
Back
The standard form of a quadratic equation is ax² + bx + c = 0, where a, b, and c are constants and a ≠ 0.
3.
FLASHCARD QUESTION
Front
How do you complete the square for the equation x² + 10x = -9?
Back
1. Move -9 to the other side: x² + 10x + 25 = 16. 2. Rewrite as (x + 5)² = 16. 3. Take the square root: x + 5 = ±4. 4. Solve for x: x = -1 or x = -9.
4.
FLASHCARD QUESTION
Front
What does the plus or minus symbol (±) indicate in solutions?
Back
The plus or minus symbol (±) indicates that there are two possible solutions: one with addition and one with subtraction.
5.
FLASHCARD QUESTION
Front
How do you derive the quadratic formula from completing the square?
Back
Starting from ax² + bx + c = 0, divide by a, rearrange, complete the square, and solve for x to derive x = (-b ± √(b² - 4ac)) / (2a).
6.
FLASHCARD QUESTION
Front
What is the vertex form of a quadratic equation?
Back
The vertex form of a quadratic equation is y = a(x - h)² + k, where (h, k) is the vertex of the parabola.
7.
FLASHCARD QUESTION
Front
What is the discriminant in a quadratic equation?
Back
The discriminant is the part of the quadratic formula under the square root: b² - 4ac. It determines the nature of the roots.
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