Graphing Quadratics in 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 about the parabola?

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 does changing 'k' in the vertex form affect the graph?

Back

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

Front

How does changing 'h' in the vertex form affect the graph?

Back

Changing 'h' shifts the graph horizontally: increasing 'h' shifts the graph to the right, while decreasing 'h' shifts it to the left.

Front

What is the vertex of the parabola given by y = -2(x + 3)² + 4?

Back

The vertex is (-3, 4).

Front

What is the maximum or minimum value of the parabola y = 3(x - 1)² + 2?

Back

The minimum value is 2, occurring at the vertex (1, 2).

Front

If a parabola opens downwards, what can be said about the value of 'a'?

Back

If a parabola opens downwards, the value of 'a' is negative.

Front

What happens to the graph of y = (x - 2)² + 1 when 'a' is multiplied by -1?

Back

The graph reflects over the x-axis, changing from opening upwards to opening downwards.

Front

Identify the vertex and direction of the parabola y = -4(x + 1)² + 5.

Back

The vertex is (-1, 5) and the parabola opens downwards.

Front

What is the effect of adding a positive number to 'k' in the vertex form?

Back

Adding a positive number to 'k' shifts the graph upwards.