If g(x) is the image of y=−3x2−12x+2 after a translation right 2 units and down 2 units, write the equation of g(x) in the standard form of a quadratic function and describe its graph.

Question

The standard form equation is g(x)=

The graph of is a parabola that opens ______ with a vertex at _______ enter the vertex as an ordered pair, including the comma.

Answer 1

f(x) = -3x²-12x+2

Need to shift f(x) 2 units right and 2 units down to get g(x). f(x-a) means a right shift by a and f(x) -b means a vertical shift down by b

g(x) = f(x-2)-2 = -3(x-2)²-12(x-2) + 2 - 2

= -3(x²-4x+4) -12x+24 + 0

= -3x²+12x-12 -12x +24

= -3x²+12

vertex of a parabola x = -b/2a = -0/-6 = 0, y = -3(0)²+12 = 12

The standard form equation is g(x)=-3x²+12

The graph of is a parabola that opens downward with a vertex at (0,12).

Answer 2

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

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

y-2-12 = -3(x^2 + 4x + 4)

y-12 = -3(x+2) has vertex (-2,14)

right 2, down 2 shifts the vertex to (2-2, 14-2) = (0,12)

it's downward opening because the x coefficient < 0

new vertex = (0,12)