Features of Quadratics Review

Front

What is a quadratic function?

Back

A quadratic function is a polynomial function of degree 2, typically expressed 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, given by the formula h = -b/(2a) and k = f(h).

Front

How do you find the line of symmetry for a quadratic function?

Back

The line of symmetry for a quadratic function is given by the equation x = -b/(2a), where a and b are the coefficients from the standard form of the function.

Front

What is the domain of a quadratic function?

Back

The domain of any 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

What does it mean for a quadratic function to have real roots?

Back

A quadratic function has real roots if its graph intersects the x-axis, which occurs when the discriminant (b² - 4ac) is greater than or equal to zero.

Front

What is the discriminant of a quadratic equation?

Back

The discriminant of a quadratic equation ax² + bx + c = 0 is given by the formula D = b² - 4ac, which determines the nature of the roots.

Front

What does a positive discriminant indicate about the roots of a quadratic equation?

Back

A positive discriminant indicates that the quadratic equation has two distinct real roots.