Compare and contrast the two quadratic equations below. In order to receive full credit, use complete sentences to describe the following:

The direction each parabola opens
The vertex of each parabola
y = x2 − 2x
y = −2x2 + 4x − 3

Question

Compare and contrast the two quadratic equations below. In order to receive full credit, use complete sentences to describe the following:

The direction each parabola opens 
The vertex of each parabola
y = x2 − 2x
y = −2x2 + 4x − 3

calculusfunctions · Answer

If given y = ax² + bx + c, the standard form of the quadratic function, then the vertex is a minimum whenever a > 0 and the parabola opens up.

The vertex is a maximum whenever a < 0 and the parabola opens down.

The vertex occurs at the point$$\left( \frac{ -b }{ 2a },y \right)$$