To find the vertex of the parabola represented by the equation f(x) = 5x² – 30x + 6, we can use the vertex formula. The x-coordinate of the vertex can be calculated using the formula:
x = -b / (2a)
In our equation, a = 5 and b = -30. Plugging these values into the formula gives us:
x = -(-30) / (2 * 5) = 30 / 10 = 3
Now that we have the x-coordinate of the vertex, we need to find the corresponding y-coordinate by substituting x back into the original equation:
f(3) = 5(3)² – 30(3) + 6
Calculating this:
- 5(3)² = 5 * 9 = 45
- -30(3) = -90
- So, f(3) = 45 – 90 + 6 = -39
Thus, the vertex of the parabola is at the point (3, -39). This means that the minimum point of the parabola occurs at x = 3, where the parabola opens upwards, as the coefficient of x² (which is 5) is positive.