#### Answer

$f(x)=4x^2+3$

#### Work Step by Step

Since the shape of the graph is a $f(x) = x^2$ we will start with that function:
$f(x)=x^2$
The first thing to notice is graph is shifted up 3 units. Shifts up or down are added to the right side of the equation. Up is positive and down is negative.
$f(x)=x^2+3$
The second thing to notice is the graph is stretched vertically by a factor of 4 because $f(x)=x^2+3$ passes through (1,4) but the graph goes through (1,7). To apply vertical stretches, multiply x term by the factor.
$f(x)=4x^2+3$