Parabolas in Vertex Form

Front

What is the vertex form of a parabola?

Back

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

Front

What does the parameter 'a' indicate in the vertex form of a parabola?

Back

The parameter 'a' indicates the direction in which the parabola opens: if 'a' is positive, the parabola opens upwards; if 'a' is negative, it opens downwards.

Front

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

Back

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

Front

What is the axis of symmetry in a parabola?

Back

The axis of symmetry is a vertical line that passes through the vertex of the parabola, given by the equation x = h.

Front

How can you find the vertex from the vertex form equation?

Back

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

Front

What is the significance of the vertex in a parabola?

Back

The vertex is the highest or lowest point of the parabola, depending on whether it opens up or down.

Front

How do you convert from standard form to vertex form?

Back

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

Front

What is the effect of changing the value of 'a' in the vertex form?

Back

Changing the value of 'a' affects the width and direction of the parabola: larger absolute values of 'a' make the parabola narrower, while smaller absolute values make it wider.

Front

What is the formula for the vertex when given a quadratic in standard form?

Back

The vertex (h, k) can be found using h = -b/(2a) and k = f(h), where f(x) is the original quadratic function.

Front

What does it mean for a parabola to be 'narrower' or 'wider'?

Back

A 'narrower' parabola has a larger absolute value of 'a', while a 'wider' parabola has a smaller absolute value of 'a'.