Graphing Quadratic Functions in Vertex Form

Front

What is the vertex form of a quadratic function?

Back

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

Front

How can you determine if a parabola opens upwards or downwards?

Back

A parabola opens upwards if the coefficient 'a' in the vertex form y = a(x - h)² + k is positive, and it opens downwards if 'a' is negative.

Front

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

Back

The vertex represents the highest or lowest point of the parabola, depending on whether it opens downwards or upwards.

Front

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

Back

The vertex can be found directly from the vertex form y = a(x - h)² + k as the point (h, k).

Front

What is the maximum value of a quadratic function in vertex form?

Back

The maximum value occurs at the vertex if the parabola opens downwards (a < 0). It is the y-coordinate of the vertex.

Front

What is the minimum value of a quadratic function in vertex form?

Back

The minimum value occurs at the vertex if the parabola opens upwards (a > 0). It is the y-coordinate of the vertex.

Front

Given the function y = - (x - 4)² - 3, what is the vertex?

Back

The vertex is (4, -3).

Front

Given the function y = (x - 3)² + 5, what is the vertex?

Back

The vertex is (3, 5).

Front

How do you convert the standard form of a quadratic function to vertex form?

Back

To convert from standard form ax² + bx + c to vertex form, complete the square.

Front

What is the axis of symmetry for a parabola in vertex form?

Back

The axis of symmetry is the vertical line x = h, where (h, k) is the vertex.