Quadratic Functions and Equations

Front

What is a quadratic function?

Back

A quadratic function is a polynomial function of degree 2, typically in the form f(x) = ax^2 + bx + c, where a, b, and c are constants and a ≠ 0.

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is ax^2 + bx + c = 0, where a, b, and c are constants.

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, found at the point (h, k) in the vertex form f(x) = a(x - h)^2 + k.

Front

How do you find the roots of a quadratic equation?

Back

The roots can be found using the quadratic formula: x = (-b ± √(b² - 4ac)) / (2a).

Front

What does the discriminant of a quadratic equation indicate?

Back

The discriminant, given by b² - 4ac, indicates the nature of the roots: if > 0, two real roots; if = 0, one real root; if < 0, no real roots.

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).

Front

What is the average rate of change of a function?

Back

The average rate of change of a function f(x) over an interval [a, b] is given by (f(b) - f(a)) / (b - a).

Front

How do you graph a quadratic function?

Back

To graph a quadratic function, identify the vertex, axis of symmetry, and intercepts, then plot points and draw a smooth curve.

Front

What transformations occur when a quadratic function is in vertex form?

Back

In vertex form f(x) = a(x - h)² + k, the graph is translated h units horizontally and k units vertically, with 'a' affecting the width and direction.

Front

What is the maximum height of a projectile modeled by a quadratic function?

Back

The maximum height can be found by determining the vertex of the quadratic function representing the projectile's height.