Completing the Square

Flashcard
•
Mathematics
•
10th - 11th Grade
•
Hard
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15 questions
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1.
FLASHCARD QUESTION
Front
What is '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, which makes it easier to find the roots.
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 expression x² + 6x?
Back
To complete the square, take half of the coefficient of x (which is 6), square it (3² = 9), and add it: x² + 6x + 9 = (x + 3)².
4.
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.
5.
FLASHCARD QUESTION
Front
What is the significance of the vertex in a quadratic function?
Back
The vertex represents the maximum or minimum point of the parabola, depending on the direction it opens.
6.
FLASHCARD QUESTION
Front
How do you find the roots of a quadratic equation using completing the square?
Back
After rewriting the equation in vertex form, set it equal to zero and solve for x to find the roots.
7.
FLASHCARD QUESTION
Front
What is the relationship between the coefficients and the roots of a quadratic equation?
Back
The sum of the roots is -b/a and the product of the roots is c/a, according to Vieta's formulas.
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