Quadratic equation solving methods and polynomial manipulation concepts tested on the SAT math section.
39 cards · basic cards · AI-written, checked twice. Edit anything.
- What is the quadratic formula?
- x = (-b ± sqrt(b² - 4ac)) / 2a
- What does the discriminant b² - 4ac tell you?
- Whether the quadratic has two real roots, one real root, or two complex roots
- What is the vertex form of a parabola?
- y = a(x - h)² + k, where (h, k) is the vertex
- If b² - 4ac > 0, how many real solutions does ax² + bx + c = 0 have?
- Two distinct real solutions
- If b² - 4ac = 0, what is true about the solutions to ax² + bx + c = 0?
- There is one repeated real solution (a double root)
- If b² - 4ac < 0, what type of solutions does ax² + bx + c = 0 have?
- Two complex conjugate solutions
- What method involves rewriting ax² + bx + c as a(x + p)² + q?
- Completing the square
- For ax² + bx + c = 0, what is the sum of the two roots?
- -b/a
- For ax² + bx + c = 0, what is the product of the two roots?
- c/a
- What is a polynomial of degree 2 called?
- A quadratic
- What is a polynomial of degree 3 called?
- A cubic
- What does the remainder theorem state?
- When a polynomial p(x) is divided by (x - a), the remainder is p(a)
- What does the factor theorem state?
- (x - a) is a factor of p(x) if and only if p(a) = 0
- What two features determine the end behavior of a polynomial?
- The degree (even or odd) and the sign of the leading coefficient
- If a polynomial has even degree and positive leading coefficient, what happens at both ends?
- Both ends extend upward to positive infinity