Increasing/Decreasing Quadratics

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 does it mean for a function to be increasing?

Back

A function is increasing on an interval if, for any two points x1 and x2 in that interval, if x1 < x2, then f(x1) < f(x2).

Front

What does it mean for a function to be decreasing?

Back

A function is decreasing on an interval if, for any two points x1 and x2 in that interval, if x1 < x2, then f(x1) > f(x2).

Front

How can you determine the intervals of increase and decrease for a quadratic function?

Back

To determine the intervals of increase and decrease, find the derivative of the function, set it to zero to find critical points, and analyze the sign of the derivative on the intervals defined by these critical points.

Front

What is the vertex of a quadratic function?

Back

The vertex of a quadratic function is the point where the function reaches its maximum or minimum value, located at the coordinates (h, k) in the vertex form f(x) = a(x - h)² + k.

Front

How does the coefficient 'a' in a quadratic function affect its graph?

Back

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

Front

What is the significance of the x-intercepts of a quadratic function?

Back

The x-intercepts (or roots) of a quadratic function are the points where the graph intersects the x-axis, indicating the values of x for which f(x) = 0.

Front

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

Back

The y-intercept of a quadratic function is the point where the graph intersects the y-axis, indicating the value of f(x) when x = 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, where a, b, and c are constants.

Front

What is the factored form of a quadratic function?

Back

The factored form of a quadratic function is f(x) = a(x - r1)(x - r2), where r1 and r2 are the roots of the function.