FOCA - 2MP Flashcard 1 Review - Solving Quadratics and i

Front

What is a quadratic equation?

Back

A quadratic equation is a polynomial equation of the form ax² + bx + c = 0, where a, b, and c are constants and a ≠ 0.

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is ax² + bx + c = 0.

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 D = b² - 4ac, which determines the nature of the roots.

Front

How do you find the roots of a quadratic equation?

Back

The roots of a quadratic equation can be found using the quadratic formula: x = (-b ± √D) / (2a), where D is the discriminant.

Front

What does it mean if the discriminant is positive?

Back

If the discriminant is positive, the quadratic equation has two distinct real roots.

Front

What does it mean if the discriminant is zero?

Back

If the discriminant is zero, the quadratic equation has exactly one real root (a repeated root).

Front

What does it mean if the discriminant is negative?

Back

If the discriminant is negative, the quadratic equation has two complex (imaginary) roots.

Front

How do you solve a quadratic equation by factoring?

Back

To solve a quadratic equation by factoring, express it in the form (px + q)(rx + s) = 0 and set each factor to zero.

Front

What is the vertex of a parabola?

Back

The vertex of a parabola is the highest or lowest point on the graph, depending on whether it opens upwards or downwards.

Front

How do you find the vertex of a quadratic function in standard form?

Back

The vertex (h, k) of a quadratic function in standard form y = ax² + bx + c can be found using h = -b/(2a) and k = f(h).