Completing the Square

Flashcard
•
Mathematics
•
9th Grade
•
Hard
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15 questions
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1.
FLASHCARD QUESTION
Front
What is the process of completing the square in a quadratic equation?
Back
Completing the square involves rewriting a quadratic equation in the form (x - p)² = q, where p and q are constants. This is done by manipulating the equation to form a perfect square trinomial.
2.
FLASHCARD QUESTION
Front
How do you find the value of 'c' to complete the square for the expression x² + bx + c?
Back
To find 'c', take half of the coefficient of x (which is b), square it, and add it to the expression. Thus, c = (b/2)².
3.
FLASHCARD QUESTION
Front
What is a perfect square trinomial?
Back
A perfect square trinomial is a quadratic expression that can be factored into the square of a binomial, such as (x - p)² or (x + p)².
4.
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.
5.
FLASHCARD QUESTION
Front
How do you solve a quadratic equation by completing the square?
Back
1. Move the constant term to the other side of the equation. 2. Complete the square on the left side. 3. Take the square root of both sides. 4. Solve for x.
6.
FLASHCARD QUESTION
Front
What is the vertex form of a quadratic function?
Back
The vertex form of a quadratic function is y = a(x - h)² + k, where (h, k) is the vertex of the parabola.
7.
FLASHCARD QUESTION
Front
What does the discriminant of a quadratic equation tell you?
Back
The discriminant (b² - 4ac) indicates the nature of the roots: if it's positive, there are two distinct real roots; if zero, one real root; if negative, two complex roots.
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