Quadratic Forms

Front

What is a quadratic form?

Back

A quadratic form is a polynomial of degree two in multiple variables, typically expressed as Q(x) = ax^2 + bxy + cy^2, where a, b, and c are constants.

Front

What is the standard form of a quadratic function?

Back

The standard form of a quadratic function is f(x) = ax^2 + bx + c, where a, b, and c are constants.

Front

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

Back

The vertex (h, k) of a quadratic function f(x) = ax^2 + bx + c can be found using h = -b/(2a) and k = f(h).

Front

What is the vertex of the function f(x) = (x - 1)² - 5?

Back

The vertex of the function f(x) = (x - 1)² - 5 is (1, -5).

Front

What does the 'a' value in a quadratic function indicate?

Back

The 'a' value in a quadratic function indicates the direction of the parabola: if a > 0, the parabola opens upwards; if a < 0, it opens downwards.

Front

What is the axis of symmetry in a quadratic function?

Back

The axis of symmetry of a quadratic function f(x) = ax^2 + bx + c is the vertical line x = -b/(2a).

Front

How can you determine if a quadratic function has a maximum or minimum value?

Back

If 'a' is positive, the function has a minimum value at the vertex; if 'a' is negative, it has a maximum value at the vertex.

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 ax² + bx + c = 0.

Front

What is the discriminant in a quadratic equation?

Back

The discriminant is the expression b² - 4ac in the quadratic formula, which determines the nature of the roots: if > 0, two real roots; if = 0, one real root; if < 0, no real roots.

Front

What is the factored form of a quadratic function?

Back

The factored form of a quadratic function is f(x) = a(x - r₁)(x - r₂), where r₁ and r₂ are the roots of the function.