Question

Compare the graph of g(x) = -3x2 - 5 with the graph of f(x) = x2

Answer 1

$g(x)=-3x^2-5$$f(x)=x^2$

Let us put g(x) in the vertex form at first

$g(x)=-3(x-0)^2-5$

-3 means the graph of f(x) stretched vertically by a scale factor 3 and also reflected across the x-axis

-5 means the graph of f(x) is translated down by 5 units

Then f(x) is stretched vertically by a scale factor 3, reflected across the x-axis and translated 5 units down