Quadratic Functions - Introduction

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 of a quadratic function is the point (h, k) where the function reaches its maximum or minimum value, found using the formula h = -b/(2a) and k = f(h).

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 equation x = h, where h is the x-coordinate of the vertex.

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 the function at x = 0, which gives the point (0, c) in the standard form f(x) = ax² + bx + c.

Front

What is the significance of the coefficient 'a' in a quadratic function?

Back

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

Front

What is the discriminant of a quadratic equation?

Back

The discriminant is the part of the quadratic formula under the square root, given by D = b² - 4ac, which determines the nature of the roots.