Flashcard 5 Solving Quadratics (All Methods)

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 quadratic formula?

Back

The quadratic formula is x = (-b ± √(b² - 4ac)) / (2a), used to find the roots of a quadratic equation.

Front

What does it mean to factor a quadratic equation?

Back

Factoring a quadratic equation means expressing it as a product of its linear factors, such as (x - p)(x - q) = 0.

Front

What is the zero product property?

Back

The zero product property states that if the product of two factors is zero, then at least one of the factors must be zero.

Front

How do you solve a quadratic equation by factoring?

Back

To solve by factoring, rewrite the equation in the form (x - p)(x - q) = 0, then set each factor to zero and solve for x.

Front

What is the greatest common factor (GCF)?

Back

The GCF is the largest factor that divides two or more numbers without leaving a remainder.

Front

How do you solve a quadratic equation using the square root method?

Back

To solve using the square root method, isolate the x² term and take the square root of both sides, remembering to consider both positive and negative roots.

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

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 formula x = -b/(2a).