Solving Quadratics

Front

What is the discriminant in a quadratic equation?

Back

The discriminant is a value that determines the nature of the roots of a quadratic equation, calculated as b² - 4ac.

Front

What does a negative discriminant indicate about the roots of a quadratic equation?

Back

A negative discriminant indicates that the quadratic equation has no real roots, only complex roots.

Front

What is another term for the solutions of a quadratic equation?

Back

Roots.

Front

How many roots does a quadratic equation have if the discriminant is zero?

Back

One real root (a repeated root).

Front

What is the standard form of a quadratic equation?

Back

The standard form is ax² + bx + c = 0, where a, b, and c are constants and a ≠ 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 is the vertex of a parabola?

Back

The vertex is the highest or lowest point of the parabola, depending on its orientation.

Front

How do you find the axis of symmetry of a parabola given by the equation y = ax² + bx + c?

Back

The axis of symmetry can be found using the formula x = -b / (2a).

Front

What is the zero product property?

Back

If the product of two factors is zero, then at least one of the factors must be zero.

Front

How can you solve a quadratic equation by factoring?

Back

Set the equation to zero, factor it into two binomials, and set each factor equal to zero to find the roots.