Question

Translated 7 units right and 2 units up.

Write an equation of the new function in vertex form.

Answer 1

An equation of the new function in vertex form is
`y=\left ( x-7 \right )^2+2`.

Explanation:

Consider parent function as
`y=x^(2)`.

According to the transformation of graph,

The function
`f\left ( x-b \right )` shifts the function to right side by b units.

So in this case, graph is translated to the right side by 7 units, so the parent function
`y=x^(2)` can be written as
`y=\left ( x-7 \right )^2`

The function
`f\left ( x \right )+b` shifts the function in upward direction by b units.

So in this case, graph is translated in upward by 2 units, so the function
`y=\left ( x-7 \right )^2` can be written as
`y=\left ( x-7 \right )^2+2`

Now vertex form of quadratic equation is given as,
`y=a\left ( x-h \right )^2+k`

So the final equation is
`y=\left ( x-7 \right )^2+2`. .