Finding the Vertex of the Parabola
The equation of the parabola is given as:
y = x² + 6x + 2
To find the vertex of a parabola represented by a quadratic equation in the standard form y = ax² + bx + c, we can use the formula for the x-coordinate of the vertex:
x = -½ * b
In our equation, we can identify:
- a = 1
- b = 6
- c = 2
Plugging the value of b into the vertex formula gives us:
x = -½ * 6 = -3
Now that we have the x-coordinate of the vertex, we need to find the corresponding y-coordinate by substituting x = -3 back into the original equation:
y = (-3)² + 6(-3) + 2
This simplifies to:
- y = 9 – 18 + 2
- y = -7
Thus, the vertex of the parabola is located at the point:
(-3, -7)
In conclusion, the vertex of the parabola described by the equation y = x² + 6x + 2 is:
Vertex: (-3, -7)