8.01 Comparing functions across representations
Interactive practice questions
Parabola $P$P is given by $y=-\frac{\left(x+2\right)^2}{4}-2$y=−(x+2)24−2 and a table of values for parabola $Q$Q is provided below.
Parabola $Q$Q:
| $x$x | $-1$−1 | $1$1 | $3$3 |
| $y$y | $-2$−2 | $-1$−1 | $-2$−2 |
Graph Parabola $Q$Q below.
Which function has the greatest maximum?
Parabola $P$P
Parabola $Q$Q
Given that we can obtain parabola $Q$Q by translating parabola $P$P to the right by $3$3 places and up by $1$1 place, how many times do the parabolas intersect?
Once
Zero times
Twice
Three times
Which function is decreasing on the domain $-2\le x\le1$−2≤x≤1?
Neither parabola $P$P nor parabola $Q$Q
Parabola $P$P and parabola $Q$Q
Parabola $P$P
Parabola $Q$Q
The parabola $P$P is given by $y=\left(x-5\right)^2+5$y=(x−5)2+5 and the parabola $Q$Q is given by $y=-2\left(x-7\right)\left(x-3\right)$y=−2(x−7)(x−3).
Parabola $P$P is given by $y=\frac{11\left(x-6\right)^2}{36}-6$y=11(x−6)236−6 and parabola $Q$Q is given by $y=\frac{13\left(x-3\right)^2}{9}-8$y=13(x−3)29−8.
The exponential function $P$P is given by $y=4\left(3^{-x}\right)$y=4(3−x). A table of approximate function values for $Q$Q is given below.