Question

I have the hardest time writing new equations for this graph

Answer 1

lets do the blue one

Answer 2

\(y=-x^2\) has vertex at \((0,0)\) and this one has vertex at \((1,4)\) so it is shifted to the right 1 unit and up 4 units.
therefore the equation is \(y=-(x-1)^2+4\)

Answer 3

if that answer is not what you are looking for, you can do some algebra to put it in standard form
\[y=-(x-1)^2+4=-(x^2-2x+1)+4\]
\[=-x^2+2x-1+4=-x^2+2x+3\]

Answer 4

others are similar, hope steps are clear

Answer 5

the first one is what i'm looking for. Thank you

Answer 6

yw

Answer 7

so is the red -(x+2)^2 + 3?