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

Back

The vertex is the point (h, k) in the equation.

Front

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

Back

Changing the 'k' value shifts the parabola up or down on the graph.

Front

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

Back

Changing the 'h' value shifts the parabola left or right on the graph.

Front

If a quadratic equation is in the form y = -2(x + 3)² + 5, what is the vertex?

Back

The vertex is (-3, 5).

Front

What does it mean if a parabola has a maximum value?

Back

A parabola has a maximum value if it opens downwards, meaning the vertex is the highest point on the graph.

Front

What does it mean if a parabola has a minimum value?

Back

A parabola has a minimum value if it opens upwards, meaning the vertex is the lowest point on the graph.

Front

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

Back

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

Front

Given the equation y = 4(x - 1)² + 2, what is the direction of the parabola?

Back

The parabola opens upwards because the 'a' value (4) is positive.