Key Features Of Quadratic Functions

Front

What is 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 quadratic function?

Back

The vertex is the highest or lowest point on the graph of a quadratic function, depending on whether it opens upwards or downwards.

Front

How do you find the x-intercepts of a quadratic function?

Back

To find the x-intercepts, set f(x) = 0 and solve for x.

Front

What is the y-intercept of a quadratic function?

Back

The y-intercept is the point where the graph intersects the y-axis, found by evaluating f(0).

Front

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

Back

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

Front

What is the axis of symmetry in a quadratic function?

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 maximum or minimum value of a quadratic function?

Back

The maximum or minimum value occurs at the vertex of the parabola, depending on the direction it opens.

Front

How do you determine the range of a quadratic function?

Back

The range can be determined by the vertex: if the parabola opens upwards, the range is [k, ∞); if it opens downwards, the range is (-∞, k], where k is the y-coordinate of the vertex.

Front

What is the discriminant in a quadratic equation?

Back

The discriminant is given by b² - 4ac and determines the nature of the roots: if > 0, two real roots; if = 0, one real root; if < 0, no real roots.