Find g(x), where g(x) is the translation 8 units up of f(x) = x^2. Write your answer in the form a(x – h)^2 + k, where a, h, and k are integers. g(x) = ______

Identify transformation rule: Identify the transformation rule for translating a function vertically. To translate a function k units up, we add k to the original function f(x).Apply transformation rule: Apply the transformation rule to the given function f(x) = x^2. Since we want to translate the function 8 units up, we set k to 8 and add it to f(x). g(x) = f(x) + 8Substitute given function: Substitute the given f(x) into the transformation equation to find g(x). g(x) = x^2 + 8Rewrite function in desired form: Rewrite g(x) in the desired form a(x - h)^2 + k. Since there is no horizontal shift, h is 0. The coefficient a is 1 because the shape of the parabola does not change, only its position. The value of k is 8, representing the vertical shift. g(x) = 1(x - 0)^2 + 8

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Find $g(x)$ , where $g(x)$ is the translation $8$ units up of $f(x) = x^2$ . $\newline$ Write your answer in the form $a(x – h)^2 + k$ , where $a$ , $h$ , and $k$ are integers. $\newline$ $g(x) =$ ______ $\newline$

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Math Problems

Algebra 2

Transformations of quadratic functions

Full solution

Q. Find

g(x)

, where

g(x)

is the translation

8

units up of

f(x) = x^2

\newline

Write your answer in the form

a(x – h)^2 + k

, where

a

h

, and

k

are integers.

\newline

g(x) =

______

\newline

Identify transformation rule: Identify the transformation rule for translating a function vertically. To translate a function $k$ units up, we add $k$ to the original function $f(x)$ .
Apply transformation rule: Apply the transformation rule to the given function $f(x) = x^2$ . Since we want to translate the function $8$ units up, we set $k$ to $8$ and add it to $f(x)$ . $\newline$ $g(x) = f(x) + 8$
Substitute given function: Substitute the given $f(x)$ into the transformation equation to find $g(x)$ . $\newline$ $g(x) = x^2 + 8$
Rewrite function in desired form: Rewrite $g(x)$ in the desired form $a(x - h)^2 + k$ . Since there is no horizontal shift, $h$ is $0$ . The coefficient $a$ is $1$ because the shape of the parabola does not change, only its position. The value of $k$ is $8$ , representing the vertical shift. $\newline$ $g(x) = 1(x - 0)^2 + 8$