Vertex Form Quadratics

Front

What is the vertex form of a quadratic equation?

Back

The vertex form of a quadratic equation is 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?

Back

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

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 axis of symmetry in a quadratic function?

Back

The axis of symmetry is a vertical line that passes through the vertex of the parabola, given by the equation x = h.

Front

How does the graph of y = x² compare to y = x² + 8?

Back

The graph of y = x² + 8 is the graph of y = x² shifted up 8 units.

Front

What transformation occurs when you change y = x² to y = (x-3)²?

Back

The graph is shifted to the right by 3 units.

Front

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

Back

A negative 'a' value reflects the parabola across the x-axis.

Front

If the vertex of a parabola is (3, 4), what is the equation in vertex form?

Back

The equation in vertex form is y = a(x-3)² + 4, where 'a' can be any non-zero value.

Front

What does it mean for a parabola to be 'stretched'?

Back

A 'stretched' parabola has a smaller absolute value of 'a', making it wider than the standard parabola.

Front

What does it mean for a parabola to be 'shrunk'?

Back

A 'shrunk' parabola has a larger absolute value of 'a', making it narrower than the standard parabola.