+18 please find the vertex, the axis of symmetry, determine whether there is a maximum or minimum value and find that value and lastly graphthe function ......of
(I) f(x)= -x^2-6x+3
+129847 f(x) = - x^2 -6x + 3
The x coordinate of the vertexx = 6 / (2 * -1) = -3 To find the y coordinate...put this back into the function =
- (-3)^2 - 6 (-3) + 3 = -9 + 18 + 3 = 12
So the vertex = ( -3, 12 )
The axis of symmetry → x = -3
This parbola turns "upside" down, so the vertex is a max
Graph : https://www.desmos.com/calculator/rzmxqd4pqh
+129847 f (x) = -x^2 -6x + 3
f (x) = - [ x^2 + 6x - 3 ] take 1/2 of 6 = 3...square it = 9....add it and subtract it
f(x) = - [ x^2 + 6x + 9 - 3 - 9 ] factor the first three terms.....simplify the last two
f(x) = - [ (x + 3)^2 - 12 ] apply the negative across the terms
f(x) = -(x +3)^2 + 12 ....this is vertex form......and the vertex is (-3, 12)
The rest of the problem is the same as before....the negative out front indicates that the parabola is inverted [upside down ]
