Vertex Form of Quadratics

Front

What is the vertex form of a quadratic equation?

Back

Front

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

Back

The value of 'a' determines the direction and width of the parabola. If 'a' is positive, the parabola opens upwards; if 'a' is negative, it opens downwards. A larger absolute value of 'a' makes the parabola narrower.

Front

What does the vertex of a parabola represent?

Back

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

Front

Back

The vertex is given directly by the coordinates (h, k) in the equation.

Front

What transformation occurs when you add a constant to the vertex form equation?

Back

Front

What transformation occurs when you change the value of 'h' in the vertex form equation?

Back

Changing the value of 'h' shifts the graph horizontally. If h increases, the graph shifts to the right; if h decreases, it shifts to the left.

Front

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

Back

Front

Back

The vertex is (3, 5).

Front

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

Back

A negative 'k' value shifts the graph of the parabola downwards by 'k' units.

Front

If a quadratic equation is given in vertex form, how can you determine if it opens upwards or downwards?

Back

If 'a' (the coefficient of the squared term) is positive, the parabola opens upwards; if 'a' is negative, it opens downwards.