Finding the Symmetry Point of 2x²: Locating the Vertex of a Quadratic Function

Given the expression of the quadratic function

Finding the symmetry point of the function

$f(x)=2x^2$

To solve this problem, we'll follow these steps:

• Identify the coefficients of the quadratic function.
• Apply the vertex formula to find the axis of symmetry and subsequently the vertex.
• Calculate the function's value at the symmetry point.

Now, let's work through each step:
Step 1: The given function is $f(x) = 2x^2$, where $a = 2$ and $b = 0$.
Step 2: The axis of symmetry for a quadratic function in the form $ax^2 + bx + c$ is given by $x = -\frac{b}{2a}$. With $b = 0$, this simplifies to $x = 0$.
Step 3: To find the vertex, calculate the function's value at $x = 0$, using $f(x) = 2x^2$.
Plugging in $x = 0$, we find:
$f(0) = 2(0)^2 = 0$.
Thus, the vertex, and hence the symmetry point of the function, is $(0, 0)$.

Therefore, the solution to the problem is $(0, 0)$.