Can someone check to see if i am doing this correctly.

Question

Okay so I have this question where they give me a graph and ask me to find out specific questions.

 

My equation for this graph given is y=-x²-2x+3

 

It ask for the vertex which after i do all the work I end up with (-1,4)

 

the range which I get y≤4

 

and then it ask for State the interval on which the function is increasing...I am not sure how to do this or if I am doing this right. When i tried to solve the problem I come up with x<4 would that be correct or am I doing this wrong?

Answer 1

Your vertex is correct

Your range is correct

Interval upon which value is increasing. not right (the answer is x < -1)

 

You have an upside down parabola (opens out the bottom.) So the vertex at -1,4 will be at the top.

on the very left side of the graph, the value of the function is negative infinity. As it gets closer and closer to -1 it is moving upwards (that is, it is increasing. After it passes x=-1, it starts heading back down (decreasing) toward negative infinity again.