Question

3.) Write the equation of a quadratic function that is shifted down 4 and horizontally compressed by 1/5

Answer 1

Answer:

$5x^2 - 4$

Step-by-step explanation:

For shifted down a function you have to follow the next structured:

$f(x) - c$

In our case is:

$x^2 - 4$

Now for compressed or shrink a graph you have to multiply by a factor in the input something like this:

$f(cx)$

In our case is:

$5x^2$

Maybe you can think, why 5 and not $\frac{1}{5}$ instead?. Well, when you multiply by $\frac{1}{5}$ this dilate or stretch the graft because the output of each value is smaller, example:

$f(x) = x^2\\g(x) = \frac{1}{5} x^2$

Then evaluate for a number, for example 5:

$f(5) = 25\\g(5) = 5$

the output of $g(x)$ is 5 steps a far from the answer of $f(x)$ 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 $5x^2 - 4$