Question

How does the graph of the quadratic function g(x)=x^2+4x+10 compare to the graph of it parents function f(x)=x^2?

Answer 1

$f(x)=x^2$

Let's add 4x to f(x) and see what happens:

$f(x)+4x=x^2+4x$

Where:

f(x) is the red one.

as you can see f(x) shifted 2 units to the left and 4 units down.

Now, let's add 10:

$f(x)+4x+10=g(x)=x^2+4x+10$

Where f(x) is the red one and g(x) is the blue one. After this, the graph shifted 10 units up.

Therefore, we can conclude, that g(x) is basically equal to f(x) but shifted 2 units to the left and 6 units up