Question

what is my teacher asking?!!! The parabola is the graph of which function? Use what you know about the parabola and vertex to help you decide.

http://roads.advancedacademics.com/contentserver/content/roadssection/277548/questions/8hw1/8hw1_q9.bmp

Long description: 0, -15. -1, -10. -2, -7. -3, -6. -4, -7. -5, -7. -6, -15.

Answer 1

i have no idea what shes asking me to do. someone explain please.... these are my options:

A. y = -2x2 + 3x + 10
B. y = x2 + 6x + 10
C. y = -x2 - 6x - 15
D. y = 2x2 + 4x + 15

what does that graph have to do with any of these equations?

Answer 2

In general, the equation


y = a(x-h)^2 + k


has the vertex (h,k) and it opens down if a < 0


In our case, the vertex is (-3, -6). So h = -3 and k = -6


This means that we go from


y = a(x-h)^2 + k


to


y = a(x-(-3))^2 + (-6)


y = a(x + 3)^2 - 6


The last thing to do is find the value of 'a'. We do this by plugging in values for x and y and solving for 'a'.


Notice that the blue parabola goes through the point (-2,-7). So x = -2 and y = -7. Plug these values in and solve for 'a'


y = a(x + 3)^2 - 6


-7 = a(-2 + 3)^2 - 6


-7 = a(1)^2 - 6


-7 = a(1) - 6


-7 = a - 6


-7 + 6 = a


-1 = a


a = -1


So the value of 'a' is a = -1


Therefore, the equation is


y = -(x+3)^2 - 6


Finally, all we need to do from here is convert to standard form


y = -(x+3)^2 - 6


y = -(x^2+6x+9) - 6


y = -x^2-6x-9 - 6


y = -x^2-6x-15


So the answer is choice C

Answer 3

I dont get it still, I suck at math. But thank you for the help.

Answer 4

Which part are you stuck at?

Answer 5

I just dont get how to start it or anything. Especially how you changed h and k and stuff.

Answer 6

h and k are simply place holders


So when I say that the vertex is (h,k) and that h = -3 and k = -6, this means that the vertex is (-3,-6)


and when I went from y = a(x-h)^2 + k to y = a(x-(-3))^2 + (-6), all I did was replace 'h' with -3 and replace 'k' with -6


Hope that clears things up. If not, let me know. Thanks.