Vertex Form

Front

What is the vertex form of a quadratic equation?

Back

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

Front

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

Back

The 'a' value determines the direction of the parabola: if 'a' is positive, the parabola opens upwards; if 'a' is negative, it opens downwards.

Front

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

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 significance of the vertex in a parabola?

Back

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

Front

How can you determine if a parabola has a maximum or minimum value?

Back

If the 'a' value in the vertex form is positive, the parabola has a minimum value; if 'a' is negative, it has a maximum value.

Front

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

Back

The vertex is (4, -3).

Front

What does it mean for a parabola to open upwards?

Back

A parabola opens upwards when the 'a' value in the vertex form is positive, indicating that the vertex is the minimum point.

Front

What does it mean for a parabola to open downwards?

Back

A parabola opens downwards when the 'a' value in the vertex form is negative, indicating that the vertex is the maximum point.

Front

How do you convert 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 vertex of the parabola given by y = 3(x + 5)² - 4?

Back

The vertex is (-5, -4).