Question

Opens down with a standard coefficient of 1. Shifted left 3 units and down 2 unitshow do I write this as an equation of a parabola that has specified features?

Answer 1

The equation of a parabola in standard form is:

`y=ax^2+bx+c`

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:

`y=-x^2+bx+c`

To shift the parabola 3 units to the left we need to add a 3 to the variable, this means that we have:

`y=-(x+3)^2+b(x+3)+c`

Finally to shift the parabola down to units we need to substract 2 to the whole parabola. therefore we have the parabola:

`y=-(x+3)^2+b(x+3)+c-2`