Quadratic Domain and Range

Front

What is the definition of a quadratic function?

Back

A quadratic function is a polynomial function of degree 2, typically written in the form f(x) = ax² + 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) = ax² + bx + c.

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 the direction it opens.

Front

How do you determine the direction a parabola opens?

Back

A parabola opens upwards if the coefficient 'a' in the quadratic function f(x) = ax² + bx + c is positive, and it opens downwards if 'a' is negative.

Front

What is the axis of symmetry in a parabola?

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).

Front

What is the domain of a quadratic function?

Back

The domain of a quadratic function is all real numbers, represented as (-∞, ∞).

Front

What is the range of a quadratic function that opens upwards?

Back

The range of a quadratic function that opens upwards is [k, ∞), where k is the y-coordinate of the vertex.

Front

What is the range of a quadratic function that opens downwards?

Back

The range of a quadratic function that opens downwards is (-∞, k], where k is the y-coordinate of the vertex.

Front

How do you find the y-intercept of a quadratic function?

Back

The y-intercept of a quadratic function can be found by evaluating f(0), which gives the point (0, c) in the function f(x) = ax² + bx + c.

Front

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

Back

The discriminant (b² - 4ac) determines the nature of the roots of the quadratic equation: if it's positive, there are two real roots; if zero, one real root; if negative, no real roots.