II know what a discriminant is; from using it, I got -40. How will this help me determine the translation?
+128408 The discriminant is
12^2 - 4 (2) (23) =
144 - 8*23 = -40 (as you found)
We need the discriminant to be = 0 for the vertex to lie on the x axis
Note that in the form ax^2 + bx + c... only "c" affects the translation vertically
Therefore we needt to have
12^2 - 4(2) c = 0
144 - 8c = 0
144 = 8c divide both sides by 8
c = 18
So...this means that if we translate the function down by (23 - 18) = 5 units....it will have its vertex on the x axis
See the graph here to confirm this : https://www.desmos.com/calculator/dtqz9ykt4k
