From the parent function of the parabola that is y = x² to y = (2x)² + 3 which can also be written as y = 4x² + 3, the parent function has been stretched 4 times, hence the 4x² which mean the value of y is 4 times larger than the original one. The parabola becomes steeper or closer to the y-axis.
In addition, the parabola is also being translated up by 3 units hence the + 3 in the new equation.
The graph will now look like this:
The red one is the parent function while the blue one is the transformation to y = 4x² + 3. The vertex of the new equation is at (0, 3).
The other points that are labeled in the graph like (-1, 7) and (1, 7) are taken if we assume x = 1 and x = -1 using the new equation.
At x = 1.
[tex]\begin{gathered} y=(2x)^2+3 \\ y=(2(1))^2+3 \\ y=4+3 \\ y=7 \end{gathered}[/tex]
At x = -1,
[tex]\begin{gathered} y=(2x)^2+3 \\ y=(2(-1))^2+3 \\ y=(-2)^2+3 \\ y=4+3 \\ y=7 \end{gathered}[/tex]
