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

Question

Given the expression of the quadratic function

Finding the symmetry point of the function

f(x)=2x2 f(x)=2x^2

Video Solution

Solution Steps

00:08 Let's find the point of symmetry for the function.
00:12 This point is where, if you fold the parabola in half, both sides match perfectly.
00:17 So, each half will be equal to the other.
00:21 First, let's examine the function's coefficients.
00:24 We'll use the special formula to find the vertex point.
00:29 Substitute the given values into the formula, and solve for X to find the point.
00:34 This X value is the point of symmetry.
00:40 And that's how we solve this problem!

Step-by-Step Solution

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)=2x2 f(x) = 2x^2 , where a=2 a = 2 and b=0 b = 0 .
Step 2: The axis of symmetry for a quadratic function in the form ax2+bx+c ax^2 + bx + c is given by x=b2a x = -\frac{b}{2a} . With b=0 b = 0 , this simplifies to x=0 x = 0 .
Step 3: To find the vertex, calculate the function's value at x=0 x = 0 , using f(x)=2x2 f(x) = 2x^2 .
Plugging in x=0 x = 0 , we find:
f(0)=2(0)2=0 f(0) = 2(0)^2 = 0 .
Thus, the vertex, and hence the symmetry point of the function, is (0,0) (0, 0) .

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

Answer

(0,0) (0,0)