Vertex Form of Quadratics

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

How do you identify the vertex from the vertex form?

Back

In the vertex form y = a(x - h)² + k, the vertex is the point (h, k).

Front

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

Back

The 'a' value determines the direction the parabola opens: if a > 0, it opens upwards; if a < 0, it opens downwards.

Front

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

Back

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

Front

How can you determine if a parabola opens up or down from its equation?

Back

If the coefficient 'a' in the vertex form y = a(x - h)² + k is positive, the parabola opens up; if negative, it opens down.

Front

What is the vertex of the parabola given by y = 3(x + 2)² - 1?

Back

The vertex is (-2, -1).

Front

If a parabola has a vertex at (4, 5), what is its axis of symmetry?

Back

The axis of symmetry is x = 4.

Front

What happens to the graph of y = x² when you multiply it by a negative number?

Back

The graph opens downward instead of upward.

Front

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

Back

Changing the 'k' value shifts the graph vertically: increasing 'k' moves it up, while decreasing 'k' moves it down.

Front

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

Back

You can convert by completing the square.