Quadratic Functions Characteristics Unit 4B Review

Front

What is a quadratic function?

Back

A quadratic function is a polynomial function of degree 2, typically in the form f(x) = ax^2 + bx + c, where a, b, and c are constants and a ≠ 0.

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.

Front

What is the vertex of a quadratic function?

Back

The vertex is the highest or lowest point of the parabola represented by the quadratic function, found at the point (h, k) in the vertex form f(x) = a(x - h)^2 + k.

Front

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

Back

The axis of symmetry can be found using the formula x = -b/(2a) from the standard form f(x) = ax^2 + bx + c.

Front

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

Back

The range depends on the direction of the parabola: if a > 0, the range is [k, ∞); if a < 0, the range is (-∞, k].

Front

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

Back

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

Front

What is the maximum height of a projectile modeled by a quadratic function?

Back

The maximum height can be found by evaluating the function at the vertex, which occurs at t = -b/(2a) for the function h(t) = -16t^2 + vt.

Front

How do you convert from standard form to vertex form?

Back

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

Front

What is the significance of the discriminant in a quadratic equation?

Back

The discriminant (D = b^2 - 4ac) indicates the nature of the roots: D > 0 means two distinct real roots, D = 0 means one real root, and D < 0 means no real roots.

Front

What is the formula for the roots of a quadratic equation?

Back

The roots can be found using the quadratic formula: x = (-b ± √(b^2 - 4ac)) / (2a).