Question

Which is one of the transformations applied to the graph of f(x) = x2 to change it into the graph of g(x) = 4x2 + 24x + 30?

A). The graph of f(x) = x2 is widened.
B). The graph of f(x) = x2 is shifted left 3 units.
C). The graph of f(x) = x2 is shifted up 30 units.
D). The graph of f(x) = x2 is reflected over the x-axis.

PLZ Answer FAST

Answer 1

Given function is,

$g(x)=4x^2+24x+30$

Complete the square of x in the right of the equation as follows:

$g(x)=4(x^2+6x)+30$

$g(x)=4(x^2+6x+9)+30-36$       (Add and subtract 36)

$g(x)=4(x+3)^2-6$

Recall the following transformations:

Vertical shifting c units downward :

If a function $y=f(x)$ is transformed into $y=f(x)-c$.

Vertical stretching by c unit :

If a function $y=f(x)$ is transformed into $y=cf(x)$, |c|>1.

Horizontal shifting c units left :

If a function $y=f(x)$ is transformed into $y=f(x+c)$.

Hence, $g(x)=4(x+3)^2-6$ is obtained after shifted $f(x)=x^2$ 6 unit down, stretched 4 unit vertically, then, shifted 3 unit left.

Therefore, the correct option is B). The graph of f(x) = $x^2$ is shifted left 3 units.