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 − 4x
y = −2x2 + 8x − 12

Answer 1

y = x² − 4x ⇒ opens upward
= x² − 4x + 4 − 4
= (x − 2)² − 4 ⇒ vertex is at (2, −4)

y = −2x² + 8x − 12 ⇒ opens downward, narrower than first one because x²-coefficient is farther away from 0
y = −2(x² − 4x + 6)
y = −2(x² − 4x + 4 + 2)
y = −2(x − 2)² − 4 ⇒ vertex is at (2, −4), same place as first one
...once you have this information, this shouldn't be a problem.