Question

Please help, I’ll mark as brainliest.

Answer 1

Step-by-step explanation:

if we translate (shift) a function g(x) to the right by k to create h(x), then h(x) creates the same functional values as g(x), but they happen now for higher x ("later", if you consider x as a kind of time).

so, e.g.

h(0) = g(0 - k)

or

g(0) = h(0 + k)

and to translate to the left by k has the opposite effect. the original results happen "earlier" on the x-axis.

so, e.g.

h(0) = g(0 + k)

or

g(0) = h(0 - k)

so, all we need to do is to replace every occurrence of x by (x - k) if shifting right, or by (x + k) if shifting left.

our graph is

10x² - 2x + 4y² - 4y = 40

so, translating this 4 units to the right gives us

10(x - 4)² - 2(x - 4) + 4y² - 4y = 40

10(x² - 8x + 16) - 2x + 8 + 4y² - 4y = 40

10x² - 80x + 160 - 2x + 8 + 4y² - 4y = 40

10x² - 82x + 4y² - 4y = -128

translating the original graph 3 units to the left gives us

10(x + 3)² - 2(x + 3) + 4y² - 4y = 40

10(x² + 6x + 9) - 2x - 6 + 4y² - 4y = 40

10x² + 60x + 90 - 2x - 6 + 4y² - 4y = 40

10x² + 58x + 4y² - 4y = -44