Parabolas Standard/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 'a' value in the vertex form indicate?

Back

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

Front

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

Back

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

Front

What is the standard form of a parabola?

Back

The standard form of a parabola is given by the equation y = ax² + bx + c.

Front

How do you convert from standard form to vertex form?

Back

To convert from standard form to vertex form, you can complete the square.

Front

What does it mean for a parabola to 'open up'?

Back

A parabola opens up when its 'a' value in the equation is positive, indicating that the arms of the parabola extend upwards.

Front

What does it mean for a parabola to 'open down'?

Back

A parabola opens down when its 'a' value in the equation is negative, indicating that the arms of the parabola extend downwards.

Front

What is the significance of the x-coordinate of the vertex?

Back

The x-coordinate of the vertex represents the axis of symmetry of the parabola.

Front

How do you find the x-coordinate of the vertex from standard form?

Back

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

Front

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

Back

Changing the 'k' value in the vertex form y = a(x - h)² + k shifts the parabola vertically up or down.