Solving Quadratics

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.

Front

What does it mean to complete the square in a quadratic equation?

Back

Completing the square involves rewriting a quadratic equation in the form (x - p)² = q, which makes it easier to solve for x.

Front

How do you factor a quadratic equation in the form x² + bx + c?

Back

To factor a quadratic equation in this form, find two numbers that multiply to c and add to b, then express it as (x - m)(x - n) where m and n are those numbers.

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.

Front

What is the discriminant in a quadratic equation, and what does it indicate?

Back

The discriminant is the part of the quadratic formula under the square root, b² - 4ac. It indicates the nature of the roots: if positive, there are two real roots; if zero, one real root; if negative, two complex roots.

Front

How can you identify the vertex of a parabola represented by a quadratic equation?

Back

The vertex of a parabola in the form y = ax² + bx + c can be found using the formula (-b/(2a), f(-b/(2a))).

Front

What is the axis of symmetry in a quadratic function?

Back

The axis of symmetry is a vertical line that divides the parabola into two mirror-image halves, given by the equation x = -b/(2a).

Front

What is the significance of the leading coefficient 'a' in a quadratic equation?

Back

The leading coefficient 'a' determines the direction of the parabola: if a > 0, it opens upwards; if a < 0, it opens downwards.

Front

How do you convert a quadratic equation from standard form to vertex form?

Back

To convert from standard form (ax² + bx + c) to vertex form (a(x - h)² + k), complete the square.

Front

What is the factored form of a quadratic equation?

Back

The factored form of a quadratic equation is expressed as a(x - m)(x - n), where m and n are the roots of the equation.