Solving Quadratics
Flashcard
•
Mathematics
•
9th - 12th Grade
•
Practice Problem
•
Hard
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16 questions
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1.
FLASHCARD QUESTION
Front
What is a quadratic equation?
Back
A quadratic equation is a polynomial equation of degree 2, typically in the form ax² + bx + c = 0, where a, b, and c are constants and a ≠ 0.
2.
FLASHCARD QUESTION
Front
What does it mean to 'complete 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.
3.
FLASHCARD QUESTION
Front
What is the quadratic formula?
Back
The quadratic formula is x = (-b ± √(b² - 4ac)) / (2a), used to find the solutions of a quadratic equation.
4.
FLASHCARD QUESTION
Front
How do you factor a quadratic expression?
Back
To factor a quadratic expression ax² + bx + c, find two numbers that multiply to ac and add to b, then rewrite the expression as (x + m)(x + n), where m and n are the found numbers.
5.
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, given by b² - 4ac. It determines the nature of the roots: if positive, two real roots; if zero, one real root; if negative, no real roots.
6.
FLASHCARD QUESTION
Front
Solve by completing the square: v² + 6v - 59 = 0
Back
v = -3 ± 2√17.
7.
FLASHCARD QUESTION
Front
Factor the quadratic expression: x² + 7x + 12
Back
(x + 3)(x + 4).
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