Vertex Form

Front

What is the shape of the graph of a quadratic function?

Back

A parabola.

Front

What is the vertex form of a quadratic equation?

Back

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

Front

How do you identify the vertex from the vertex form of a quadratic equation?

Back

The vertex is given by the point (h, k) in the equation y = a(x - h)² + k.

Front

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

Back

The 'a' value indicates the direction of the opening (upward if a > 0, downward if a < 0) and the width of the parabola.

Front

If a quadratic function has a vertex at (2, -3), what is the vertex form of the equation if a = 1?

Back

y = (x - 2)² - 3.

Front

What is the standard form of a quadratic equation?

Back

y = ax² + bx + c.

Front

How can you convert from vertex form to standard form?

Back

Expand the vertex form equation y = a(x - h)² + k to get y = ax² - 2ahx + (ah² + k).

Front

What is the axis of symmetry for 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 do you determine if a parabola opens upward or downward from its equation?

Back

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

Front

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

Back

Changing 'a' affects the width and direction of the parabola; larger |a| makes it narrower, smaller |a| makes it wider.