Question

(x)= -x^2-3x+6
find the vertex, axis of symmetry, max or min value, range, interval increasing and decreasing, solve the equation f(x)=0

Answer 1

f(x) = - x^2 - 3x + 6 .
a) y-intercept --> x = 0 -> y = 6
x- intercepts -> y = 0 -> Use formula to solve y = -x^2 - 3x + 6 = 0
D = 9 + 24 = 32 = 16*2 --> VD = 4V2 and VD = -4V2
2 real roots: x1 = -3/2 + 4V2/2 = (-3 + 4V2)/2 = 1.32,
and x2 = (-3 - 4V2)/2 = -4.32
b) The axis is at x = -b/2a = 3/-2 = -3/2
Since a is negative the parabola is downward. There is a max with vertex at x = -3/2
y of vertex: y (ver.) = -(9/4) + 9/2 + 6 = 33/4
c) Function y increases from -infinity to x = -3/2
Function y decreases from x =-3/2 to -infinity