Finding the Vertex of a Quadratic Function
The vertex of a quadratic function in the standard form f(x) = ax² + bx + c can be found using the vertex formula, which is given as:
x = -b / (2a)
In your case, the function is f(x) = x² + 8x + 3. Here, we identify:
- a = 1
- b = 8
- c = 3
Now, we can plug in the values of a and b into the vertex formula:
x = -8 / (2 * 1) = -8 / 2 = -4
So the x-coordinate of the vertex is -4.
Next, we need to find the corresponding y-coordinate by substituting x = -4 back into the function:
f(-4) = (-4)² + 8 * (-4) + 3
f(-4) = 16 – 32 + 3
f(-4) = -16 + 3 = -13
Thus, the y-coordinate of the vertex is -13.
Conclusion
Therefore, the vertex of the function f(x) = x² + 8x + 3 is at the point:
(-4, -13).