Locate the Symmetry Point of the Quadratic Function f(x)=3+3x^2

Given the expression of the quadratic function

Finding the symmetry point of the function

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

Video Solution

Solution Steps

00:00 Find the point of symmetry in the function

00:03 Point of symmetry is the point where if you fold the parabola in half

00:06 The halves will be equal to each other

00:11 Let's examine the function's coefficients

00:22 We'll use the formula to calculate the vertex point

00:25 We'll substitute appropriate values according to the given data and solve for X at the point

00:30 This is the X value at the point of symmetry

00:33 Now let's substitute this X value in the function to find the Y value at the point

00:42 This is the Y value at the point of symmetry

00:48 And this is the solution to the question

Step-by-Step Solution

To solve this problem, we need to find the symmetry point of the quadratic function given by $f(x) = 3 + 3x^2$ .

Step 1: Identify the type of quadratic equation. Here, it's $ax^2 + bx + c$ where $a = 3$ , $b = 0$ , and $c = 3$ .
Step 2: Use the formula for the symmetry point $x = -\frac{b}{2a}$ . Since $b = 0$ , the formula simplifies to $x = 0$ .
Step 3: Calculate the y-coordinate by substituting $x = 0$ into the original function: $f(0) = 3(0)^2 + 3 = 3$ .

Thus, the symmetry point (also the vertex of the parabola) is $(0, 3)$ .

Therefore, the solution to the problem is $(0, 3)$ .