Key Features of Quadratic Functions

Front

What is a quadratic function?

Back

A quadratic function is a polynomial function of degree 2, typically 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

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 range of a quadratic function that opens upwards?

Back

The range is all real numbers greater than or equal to the y-coordinate of the vertex.

Front

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

Back

The range is all real numbers less than or equal to the y-coordinate of the vertex.

Front

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

Back

The x-intercepts can be found by setting f(x) = 0 and solving the equation ax² + bx + c = 0.

Front

What is the significance of the y-intercept in a quadratic function?

Back

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

Front

What is the discriminant in a quadratic equation?

Back

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