f r(x) is the image of y=−3x^2−30x+2 after a translation right 3 units and down 2 units, write the equation of r(x) in the standard form of a quadratic function and describe its graph.

Question

The standard form equation is r(x)= ________

The graph of is a parabola that opens _______ with a vertex at _________

Answer 1

first you need transfer the equation to vertex form using completing the squares

y=-3(x^2+10x+25)+2+75

y=-3(x+5)^2+77

then since it translate right 3 down 2, the new equation should be:

y=-3(x+5-3)^2+77-2

y=-3(x+2)^2+75 this is vertex form.

y=-3(x^2+4x+4)+75

y=-3x^2-12x-12+75

y=-3x^2-12x+63 this is the standard form, it opens downward with vertex (-2,75)