Question

what is the maximum y value on the graph -x^2+4x+4

Answer 1

the maximum value of y is at the vertex of this parabola. do you know how to find the vertex?

Answer 2

Is this a calculus class?

Answer 3

algebra. is the vertex (2,8) with the parabola opening downward

Answer 4

so the max y value is the y coordinate of the vertex.

Answer 5

Thank you. I think the vertex ends up being (2,16) so my answer would be 16

Answer 6

wait

Answer 7

the x coordinate of the vertex is found by -b/2a which in this case b=4 and a=-1, thus the x coordinate of the vertex is 2. if you plug 2 back into your original function, so x^2+4x_4|x=2, you do not get 16. I thought you were saying that the vertex was (2,8) earlier.. and that is right.. with the parabola opening downward since the coefficient of x is negative. had it been positive you would end up with a minimum value.

Answer 8

so 8 is the maximum y-value of x^2+4x+4

Answer 9

hope that wasn't too confusing.

Answer 10

nope makes sense, thank you. The second time I did it I forgot a negative sign