The 'template' for a quadratic function is:
[tex]f(x) = ax^{2}+bx+c[/tex], where a is the vertical stretch/compression factor.
If the a in f(x) is 2/5, then vertically stretching the function is done by multiplying the function by 2, making:
[tex]g(x) = 2(\frac{2}{5}x^{2}-2)\\g(x)=\frac{4}{5}x^{2}-2[/tex]