Everything QUADRATICS

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 is all real numbers greater than or equal to the minimum value of the function, often expressed as [k, ∞) where k is the vertex's y-coordinate.

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 maximum value of the function, often expressed as (-∞, k] where k is the vertex's y-coordinate.

Front

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

Back

Set the quadratic equation equal to zero and solve for x. The solutions are the x-intercepts.

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) for the quadratic equation ax² + bx + c.

Front

What does it mean if a quadratic function has no real solutions?

Back

It means the graph of the function does not intersect the x-axis, indicating that the discriminant (b² - 4ac) is less than zero.

Front

What is the vertex of a quadratic function?

Back

The vertex is the highest or lowest point of the parabola, found at the coordinates (h, k) where h = -b/(2a) and k is the function's value at h.

Front

What is the standard form of a quadratic function?

Back

The standard form is f(x) = ax² + bx + c, where a, b, and c are constants.

Front

What is the vertex form of a quadratic function?

Back

The vertex form is f(x) = a(x - h)² + k, where (h, k) is the vertex of the parabola.

Front

How can you determine if a quadratic function opens upwards or downwards?

Back

If the coefficient 'a' in the standard form ax² + bx + c is positive, the parabola opens upwards; if 'a' is negative, it opens downwards.