Chapter 7.5, Problem 17OE

To determine

How to shift the graph of function $y=2x^2$ to obtain the graph of function $y+4=2{\left(x-1\right)}^2$ .

Answer to Problem 17OE

The graph of the function can be obtained by shifting the graph $y=2x^2$ , $1$ unit right and $4$ units downwards.

Explanation of Solution

Given information: The given function whose graph has to shift is,

  $y=2x^2\mathrm{....}\left(1\right)$

Calculation: Since (1) represents a parabola of the form $y-k=a{\left(x-h\right)}^2$ which has the vertex $\left(0,0\right)$ . Now to obtain the graph of the function $y+4=2{\left(x-1\right)}^2$ which is also of the form $y-k=a{\left(x-h\right)}^2$ can be obtained by shifting the graph $y=2x^2$ , $1$ unit right and $4$ units downwards because the function $y+4=2{\left(x-1\right)}^2$ represents a parabola having vertex $\left(1,-4\right)$ . Hence in this way the graph of the function can be obtained.