Apply the vertex formula: x=-b/(2a)x=−b2a, where a=-1a=−1 and b=9b=9
Thus,
x=-(9)/(2(-1))x=−92(−1)
x=9/2x=92
We must now find the yy-value for the vertex which we can find by substituting 9/292 for xx in the given equation y=-x^2+9x-8y=−x2+9x−8. So...
-(9/2)^2+9(9/2)-8−(92)2+9(92)−8
y=-81/4+81/2-8y=−814+812−8
Find the LCD of 4,24,2 and 11; that is 44
y=-81/4+(81times2)/(2times2)-(8times4)/(1times4)y=−814+81×22×2−8×41×4
y=-81/4+162/4-32/4y=−814+1624−324
y=(-81+162-32)/4y=−81+162−324
y=49/4y=494
And so the vertex is (9/2,49/4)(92,494)
