Parts of Quadratic Functions

Front

What is a quadratic function?

Back

A quadratic function is a polynomial function of degree 2, typically in the form of 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 function?

Back

The standard form of a quadratic function is f(x) = ax^2 + 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 the direction it opens.

Front

How do you find the vertex of a quadratic function in standard form?

Back

The vertex can be found using the formula: x = -b/(2a) and then substituting x back into the function to find the y-coordinate.

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 equation x = -b/(2a).

Front

What does it mean if a quadratic function opens upwards?

Back

If a quadratic function opens upwards, the coefficient 'a' is positive, and the vertex represents the minimum point of the function.

Front

What does it mean if a quadratic function opens downwards?

Back

If a quadratic function opens downwards, the coefficient 'a' is negative, and the vertex represents the maximum point of the function.

Front

How do you determine if the vertex is a maximum or minimum?

Back

If 'a' is positive, the vertex is a minimum; if 'a' is negative, the vertex is a maximum.

Front

What are the roots of a quadratic function?

Back

The roots (or zeros) of a quadratic function are the x-values where the function equals zero, representing the points where the graph intersects the x-axis.

Front

How can you find the roots of a quadratic function?

Back

Roots can be found using factoring, completing the square, or the quadratic formula: x = (-b ± √(b² - 4ac)) / (2a).