Question

The graphs below have the same shape. Complete the equation of the bluegraph. Enter exponents using the caret (1); for example, enter x2 as x^2. Donot include "G(x) ="

Answer 1

The equation of the graph in red is given by

$f(x)=x^2$

Let us find the equation of the graph in blue.

Notice that the blue graph is horizontally translated to the right by 3 units.

The rule for horizontal translation to the right is given by

$g(x)=(x-d)^2$

For the given case, the translation is 3 units so the equation becomes

$g(x)=(x-3)^2$

Also, notice that the blue graph is vertically translated upward by 1 unit.

The rule for vertical translation upward is given by

$g(x)=x^2+c$

For the given case, the translation is 1 unit so the equation becomes

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

Finally, combining both of the translations, the equation of the blue graph becomes

$g(x)=(x-3)^2+1$