Quadratic Functions & Vertex Form

Front

What is a quadratic function?

Back

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

Front

What is vertex form of a quadratic function?

Back

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

Front

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

Back

The vertex of a quadratic function in vertex form f(x) = a(x - h)² + k is the point (h, k).

Front

What does the 'a' value in the vertex form indicate?

Back

The 'a' value in the vertex form indicates the direction of the parabola (upward if a > 0, downward if a < 0) and the width of the parabola (narrower if |a| > 1, wider if |a| < 1).

Front

How can you convert standard form to vertex form?

Back

To convert from standard form f(x) = ax² + bx + c to vertex form, you can complete the square.

Front

What is the axis of symmetry in a quadratic function?

Back

The axis of symmetry of a quadratic function is a vertical line that passes through the vertex, given by the equation x = h, where (h, k) is the vertex.

Front

What is the significance of the vertex in a quadratic function?

Back

The vertex represents the maximum or minimum point of the parabola, depending on the direction it opens.

Front

How do you determine if a quadratic function opens upwards or downwards?

Back

A quadratic function opens upwards if the coefficient 'a' is positive and downwards if 'a' is negative.

Front

What is 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, found by evaluating f(0).

Front

What is the formula for finding the x-coordinate of the vertex?

Back

The x-coordinate of the vertex can be found using the formula x = -b/(2a) from the standard form f(x) = ax² + bx + c.