Question

Hello, I am having some trouble completing the parabola. How do I find the other points. Can someone please help me step by step in detail please?

Answer 1

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.

`\begin{gathered} y=(2x)^2+3 \\ y=(2(1))^2+3 \\ y=4+3 \\ y=7 \end{gathered}`

At x = -1,

`\begin{gathered} y=(2x)^2+3 \\ y=(2(-1))^2+3 \\ y=(-2)^2+3 \\ y=4+3 \\ y=7 \end{gathered}`