The equation of a parabola in standard form is:
[tex]y=ax^2+bx+c[/tex]where a is the standard coefficient. We know that this has to be 1 and that the parabola opens down. This means that our parabola has the form:
[tex]y=-x^2+bx+c[/tex]To shift the parabola 3 units to the left we need to add a 3 to the variable, this means that we have:
[tex]y=-(x+3)^2+b(x+3)+c[/tex]Finally to shift the parabola down to units we need to substract 2 to the whole parabola. therefore we have the parabola:
[tex]y=-(x+3)^2+b(x+3)+c-2[/tex]