To find the vertex of a quadratic function, you can use the formula derived from the function’s standard form, which is written as f(x) = ax² + bx + c.
The x-coordinate of the vertex can be calculated using the formula x = -b / (2a). Once you have the x-coordinate, you can substitute this value back into the original function to find the corresponding y-coordinate. This gives you the vertex as the point (x, f(x)).
For example, if you have a quadratic function like f(x) = 2x² + 4x + 1, you would first identify a and b. Here, a = 2 and b = 4. Plugging these values into the formula for the x-coordinate gives:
x = -4 / (2 * 2) = -4 / 4 = -1
Next, substitute x = -1 back into the function to find the y-coordinate:
f(-1) = 2(-1)² + 4(-1) + 1 = 2(1) – 4 + 1 = 2 – 4 + 1 = -1
Thus, the vertex of this quadratic function is at the point (-1, -1).