quadratic function attributes

Front

What is a quadratic function?

Back

A quadratic function is a polynomial function of degree 2, typically in the form f(x) = ax² + bx + c, where a, b, and c are constants and a ≠ 0.

Front

What are the key attributes of a quadratic function?

Back

The key attributes include the vertex, axis of symmetry, x-intercepts (roots), y-intercept, and the direction of the parabola (opening up or down).

Front

How do you find the vertex of a quadratic function?

Back

The vertex can be found using the formula x = -b/(2a) for the x-coordinate, and then substituting this value 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 passes through the vertex of the parabola, given by the equation x = -b/(2a).

Front

What are x-intercepts of a quadratic function?

Back

X-intercepts are the points where the graph of the function crosses the x-axis, found by setting f(x) = 0 and solving for x.

Front

What is the y-intercept of a quadratic function?

Back

The y-intercept is the point where the graph crosses the y-axis, found by evaluating the function at x = 0.

Front

How do you determine the direction a parabola opens?

Back

The direction of the parabola is determined by the coefficient 'a' in the quadratic function: if a > 0, it opens upwards; if a < 0, it opens downwards.

Front

What is the standard form of a quadratic function?

Back

The standard form is f(x) = ax² + bx + c, where a, b, and c are constants.

Front

What is the vertex form of a quadratic function?

Back

The vertex form is f(x) = a(x - h)² + k, where (h, k) is the vertex of the parabola.

Front

How can you convert from standard form to vertex form?

Back

You can convert by completing the square on the standard form equation.