Answer:
Step-by-step explanation:
We can recognize that the parent function for all of these graphs is going to be y=x^2. What this means is that we can graph y=x^2 and then apply transformations to it to get to all of these new graphs.
1. y = -x^2 + 5
We can see that the coefficient of the x^2 term is negative which tells us that the graph will now open downwards.
We also know that we are adding 5 on the outside of the argument which means it affect vertical shift. Therefore, we will be moving 5 units up.
2. y = x^2 - 4
We can see that the only change made to this equation is subtracting 4 on the outside of the squared part of the equation. Again, this signifies vertical movement, but since it's negative we will be moving the entire y = x^2 graph down 4 units.
3. y = -x^2 - 1
What do you notice about this graph?
- negative coefficient
- subtracting 1 outside of the argument
What do these mean?
- negative coefficient: opens downwards
- subtracting 1: move entire y = x^2 graph down 1 unit
