Question

the graph shows g(x), which is a translation of f(x) = x². write the function rule for g(x). write your answer in the form a(x - h)² + k, where a, h, and k are integers or simplified fractions. g(x) = (x²+

Explanation:

Step1: Identify the vertex - form of a parabola

The vertex - form of a parabola is $y = a(x - h)^2 + k$, where $(h,k)$ is the vertex of the parabola. For the parent function $f(x)=x^{2}$, the vertex is $(0,0)$.

Step2: Determine the vertex of $g(x)$

From the graph, the vertex of $g(x)$ is $(1,1)$. So, $h = 1$ and $k = 1$.

Step3: Determine the value of $a$

Since there is no vertical stretch or compression (the shape of the parabola is the same as $y = x^{2}$), $a = 1$.

Step4: Write the function rule for $g(x)$

Substitute $a = 1$, $h = 1$, and $k = 1$ into the vertex - form. We get $g(x)=(x - 1)^2+1=x^{2}-2x + 1+1=x^{2}-2x+2$.

Answer:

$g(x)=(x - 1)^2+1$