Finding the Symmetry Point of the Quadratic Function f(x) = 3 - 5x²

Given the expression of the quadratic function

Finding the symmetry point of the function

$f(x)=3-5x^2$

Video Solution

Solution Steps

00:00 Find the symmetry point in the function

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

00:06 The halves will be equal to each other

00:10 We'll examine the function's coefficients

00:21 We'll use the formula to calculate the vertex point

00:24 We'll substitute appropriate values according to the given data and solve for X at the point

00:31 This is the X value at the symmetry point

00:35 Now we'll substitute this X value in the function to find the Y value at the point

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

00:48 And this is the solution to the question

Step-by-Step Solution

To find the symmetry point of the quadratic function $f(x) = 3 - 5x^2$ , we follow these steps:

Identify that the function is in the form $f(x) = ax^2 + bx + c$ , where $a = -5$ , $b = 0$ , and $c = 3$ .
The x-coordinate of the symmetry point, also known as the vertex, is given by the formula $x = -\frac{b}{2a}$ .
Substitute the values: $x = -\frac{0}{2(-5)} = 0$ .
Calculate the y-coordinate by substituting $x = 0$ into the function: $f(0) = 3 - 5(0)^2 = 3$ .
Hence, the symmetry point of the function is $(0, 3)$ .

Therefore, the symmetry point of the function $f(x) = 3 - 5x^2$ is $(0, 3)$ .