Question

The graphs below have the same shape. What is the equation of the bluegraph?

Answer 1

Horizontal translation for a parabola is changed by the value of a variable, h, that is subtracted from x before the squaring operation.

Our reference parabola has the following equation:

`F(x)=x^2`

And the equation that includes a horizontal translation looks like this:

`G(x)=(x-h)^2`

The sign of h is determined by whether the translated parabola is on the right (positive sign) or on the left (negative sign) side of the reference parabola, in this case, the vertex of the parabola is translated 3 units to the left, then h equals -3, replacing this value for h, we get:

`\begin{gathered} G(x)=(x-(-3))^2 \\ G(x)=(x+3)^2 \end{gathered}`

Then, the correct answer is option D, G(x) = (x+3)^2