Answer:
[tex]y= x^2 -x+6[/tex]
Step-by-step explanation:
The equation for a parabola defined as a conic section is:
[tex](x-h)^2=4P(y-k)[/tex]
where:
We can identify the following variable values from the given information:
Plugging these into the equation, we get:
[tex]\boxed{(x-2)^2=4(y+5)}[/tex]
This can be converted to standard form by solving for y:
[tex]x^2-4x+4=4y+20[/tex]
[tex]4y=4x^2-4x-16[/tex]
[tex]\boxed{y= x^2 -x-4}[/tex]