How do I determine the vertex of the graph f(x) = -2x2 + 12x - 17
To find the vertex of this parabola, we want to employ
-b
2a
this will give us the x-coordinate of the vertex (x, y)
ax2 + bx - c
-2x2 + 12x - 17
- 12
2(-2)
=
- 12
- 4
= 3
To find the y-coordinate of the vertex, we'll plug the x back into the original equation
-2(3)2 +
12(3) - 17
- 18 + 36 - 17 = 1
the vertex of this parabola is at (3, 1)
-b
2a
this will give us the x-coordinate of the vertex (x, y)
ax2 + bx - c
-2x2 + 12x - 17
- 12
2(-2)
=
- 12
- 4
= 3