Answer:
[tex]5x^2 - 4[/tex]
Step-by-step explanation:
For shifted down a function you have to follow the next structured:
[tex]f(x) - c[/tex]
In our case is:
[tex]x^2 - 4[/tex]
Now for compressed or shrink a graph you have to multiply by a factor in the input something like this:
[tex]f(cx)[/tex]
In our case is:
[tex]5x^2[/tex]
Maybe you can think, why 5 and not [tex]\frac{1}{5}[/tex] instead?. Well, when you multiply by [tex]\frac{1}{5}[/tex] this dilate or stretch the graft because the output of each value is smaller, example:
[tex]f(x) = x^2\\g(x) = \frac{1}{5} x^2[/tex]
Then evaluate for a number, for example 5:
[tex]f(5) = 25\\g(5) = 5[/tex]
the output of [tex]g(x)[/tex] is 5 steps a far from the answer of [tex]f(x)[/tex] this in a graph is illustrate as a stretching.
So the opposite happen when you multiply by a integer number, the graph is compressed because the output take the "faster steps".
So combine the two transformation and get [tex]5x^2 - 4[/tex]
