BW - 8.1-8.8 Review of Graphing & Solving Quadratics

Front

What is the discriminant of a quadratic equation?

Back

The discriminant is given by the formula D = b² - 4ac, where a, b, and c are coefficients of the quadratic equation ax² + bx + c = 0. It determines the nature of the roots.

Front

What does a positive discriminant indicate?

Back

A positive discriminant indicates that the quadratic equation has two distinct real roots.

Front

What does a zero discriminant indicate?

Back

A zero discriminant indicates that the quadratic equation has exactly one real root (a repeated root).

Front

What does a negative discriminant indicate?

Back

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

Front

What is the vertex of a quadratic function in standard form?

Back

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

Front

How do you find the axis of symmetry for a quadratic function?

Back

The axis of symmetry for a quadratic function y = ax² + bx + c is given by the line x = -b/(2a).

Front

What is the Quadratic Formula?

Back

The Quadratic Formula is used to find the roots of a quadratic equation and is given by: x = (-b ± √(b² - 4ac)) / (2a).

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 is the factored form of a quadratic equation?

Back

The factored form of a quadratic equation is expressed as a(x - r₁)(x - r₂) = 0, where r₁ and r₂ are the roots of the equation.

Front

How do you determine if a quadratic function opens upwards or downwards?

Back

A quadratic function opens upwards if the coefficient 'a' is positive and opens downwards if 'a' is negative.