Question

On a coordinate plane, two parabolas open up. The solid-line parabola, labeled f of x, goes through (negative 2, 4), has a vertex at (0, 0), and goes through (2, 4). The dashed-line parabola, labeled g of x, goes through (negative 6, 10), has a vertex at (negative 4, 6), and goes through (negative 2, 10).
What is the equation of the translated function, g(x), if

f(x) = x2?


g(x) = (x – 4)2 + 6

g(x) = (x + 6)2 – 4

g(x) = (x – 6)2 – 4

g(x) = (x + 4)2 + 6

Answer 1

The answer is D  just took the test.

Answer 2

Answer:

$y = (x+4)^{2}+6$

Step-by-step explanation:

The parabola with vertex at point (h,k) is described by the following model:

$y - k = C\cdot (x-h)^{2}$

The equation which satisfies the conditions described above:

$y - 6 = (x+4)^{2}$

$y = (x+4)^{2}+6$

The two points are evaluated herein:

x = -6

$y =(-6+4)^{2}+6$

$y = (-2)^{2}+6$

$y = 4 + 6$

$y = 10$

x = -2

$y = (-2+4)^{2}+6$

$y = 2^{2} + 6$

$y = 4 + 6$

$y = 10$

The equation of the translated function is $y = (x+4)^{2}+6$.