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

How does the value of 'a' in the vertex form affect the graph of the parabola?

Back

The value of 'a' determines the direction of the parabola (upward if a > 0, downward if a < 0) and the width of the parabola (narrower if |a| > 1, wider if |a| < 1).

Front

What does the vertex of a parabola represent?

Back

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

Front

How do you find the vertex from the vertex form y = a(x - h)² + k?

Back

The vertex can be directly identified as (h, k) from the vertex form.

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

If a parabola opens upwards, what can be said about its vertex?

Back

If a parabola opens upwards, the vertex is the minimum point of the graph.

Front

If a parabola opens downwards, what can be said about its vertex?

Back

If a parabola opens downwards, the vertex is the maximum point of the graph.

Front

What transformation occurs when the equation y = x² is changed to y = (x - 4)²?

Back

The graph is shifted right by 4 units.

Front

What transformation occurs when the equation y = x² is changed to y = (x + 3)²?

Back

The graph is shifted left by 3 units.

Front

How do you determine if a parabola opens up or down from its vertex form?

Back

If 'a' is positive, the parabola opens up; if 'a' is negative, it opens down.