Flashcard library · Precalculus
Algebra: Quadratic Equations
This flashcard deck covers essential concepts for understanding and solving quadratic equations in Algebra. Master key definitions, standard forms, solution methods like factoring and the quadratic formula, and interpret the discriminant and graphs.
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What makes an equation quadratic?
Its highest power of the variable is 2.
What is the standard form of a quadratic equation?
ax² + bx + c = 0, with a ≠ 0.
How many roots does a quadratic equation have?
Two, counting repeats and complex roots — they may be equal or non-real.
What are three methods for solving a quadratic?
Factoring, completing the square and the quadratic formula.
What is the quadratic formula?
x = (−b ± √(b² − 4ac)) / 2a.
When is the quadratic formula the best choice?
When the quadratic does not factor easily — it solves any quadratic.
What is the discriminant?
b² − 4ac, the expression under the square root in the quadratic formula.
What does a positive discriminant mean?
Two distinct real roots.
What does a zero discriminant mean?
One repeated real root.
What does a negative discriminant mean?
Two complex conjugate (non-real) roots, and no x-intercepts.
What shape is the graph of a quadratic function?
A parabola.
What is the vertex of a parabola?
Its turning point — the minimum if a > 0, the maximum if a < 0.
What is the x-coordinate of the vertex of y = ax² + bx + c?
x = −b / 2a.
What do the real roots of a quadratic correspond to on its graph?
The x-intercepts (zeros) of the parabola.
What is the sum of the roots of ax² + bx + c = 0?
−b/a.
What is the product of the roots of ax² + bx + c = 0?
c/a.