Maximum and Minimum Values of Quadratic Functions

Front

What is a quadratic function?

Back

A quadratic function is a polynomial function of degree 2, typically in the form y = 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 y = ax² + bx + c.

Front

What is the vertex of a quadratic function?

Back

The vertex is the highest or lowest point of the parabola represented by the quadratic function, depending on whether it opens upwards or downwards.

Front

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

Back

The axis of symmetry can be found using the formula x = -b/(2a), where a and b are coefficients from the quadratic equation in standard form.

Front

What does it mean for a quadratic function to have a maximum value?

Back

A quadratic function has a maximum value when it opens downwards (a < 0), and the vertex represents the highest point on the graph.

Front

What does it mean for a quadratic function to have a minimum value?

Back

A quadratic function has a minimum value when it opens upwards (a > 0), and the vertex represents the lowest point on the graph.

Front

How do you determine the y-intercept of a quadratic function?

Back

The y-intercept can be found by evaluating the function at x = 0, which gives the point (0, c) in the standard form y = ax² + bx + c.

Front

What is the significance of the discriminant in a quadratic equation?

Back

The discriminant (D = b² - 4ac) 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.

Front

What is the formula for finding the maximum or minimum value of a quadratic function?

Back

The maximum or minimum value can be found by substituting the x-coordinate of the vertex (x = -b/(2a)) back into the function.

Front

What is the general shape of a quadratic function's graph?

Back

The graph of a quadratic function is a parabola, which can open upwards or downwards.