The graph of f(x) = x2 is translated to form g(x) = (x – 5)2 + 1.

On a coordinate plane, a parabola, labeled f of x, opens up. It goes through (negative 2, 4), has a vertex at (0, 0), and goes through (2, 4).

Which graph represents g(x)?

On a coordinate plane, a parabola opens up. It goes through (2, 10), has a vertex at (5, 1), and goes through (8, 10).
On a coordinate plane, a parabola opens up. It goes through (2, 8), has a vertex at (5, negative 11), and goes through (8, 8).
On a coordinate plane, a parabola opens up. It goes through (negative 8, 10), has a vertex at (negative 5, 1), and goes through (negative 2, 10).
On a coordinate plane, a parabola opens up. It goes through (negative 8, 8), has a vertex at (negative 5, negative 11), and goes through (negative 2, 8).

If the function f(x) translated horizontally to the right by h units, then its image is g(x) = f(x - h)
If the function f(x) translated horizontally to the left by h units, then its image is g(x) = f(x + h)
If the function f(x) translated vertically up by k units, then its image is g(x) = f(x) + k
If the function f(x) translated vertically down by k units, then its image is g(x) = f(x) - k

∵ The graph of f(x) = x² is translated to form g(x) = (x - 5)² + 1

∵ x² is changed to (x - 5)² and f(x) is added by 1

∴ The graph of f(x) is translated 5 units right and 1 unit up

∵ The parabola it goes through (-2, 4), has a vertex at (0, 0),

and goes through (2, 4)

- The x-coordinate of each point is added by 5 and the y-coordinate

of each point is add by 1

∴ The image of the point (-2 , 4) = (-2 + 5 , 4 + 1) = (3 , 5)

∴ The image of its vertex (0 , 0) = (0 + 5 , 0 + 1) = (5 , 1)

∴ The image of the point (2 , 4) = (2 + 5 , 4 + 1) = (7 , 5)

∴ The graph represents g(x) has a vertex point at (5 , 1)

The first answer only has a vertex at (5 , 1) let us check that the

parabola goes through points (2 , 10) and (8 , 10) by substituting

their x-coordinates in g(x) if the answer equal the y-coordinates,

then the points lie on the parabola

∵ x = 2 and y = 10

∴ g(x) = (2 - 5)² + 1 = (-3)² + 1 = 9 + 1 = 10 ⇒ same value of y-coordinate

∴ Point (2 , 10) lies in the parabola

∵ x = 8 and y = 10

∴ g(x) = (8 - 5)² + 1 = (3)² + 1 = 9 + 1 = 10 ⇒ same value of y-coordinate

∴ Point (8 , 10) lies in the parabola

The graph represents g(x) is:

" On a coordinate plane, a parabola opens up. It goes through (2, 10), has a vertex at (5, 1), and goes through (8, 10) "

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brycebenton brycebenton · Answer 2 · 2020-11-18T16:39:27+01:00

Answer:

Basically,

it's A, your first option

Step-by-step explanation:

I hope i simplified things for ya!

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