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As far as the concavity is concerned you can obviously differentiate (as a colleague already did), or you can instantly observe that the quadratic equation that you have is -3x^2+...... (I don't care about the rest). The coefficient of x^2 is a negative number, this instantly means that we have an "n" curve, therefore a concave down function. As far as the x-intercept is concerned, we already know that on the x-axis, y is always zero, and y=f(x). -3(x+5)(x-11)=0.  We have a product that involves two brackets. Since -3 cannot be zero, inevitably one of the brackets has to be equal to zero, which means x+5=0 or x-11=0 which gives you x=-5 or x=11. Thus, you have the points A(-5,0) and B(11,0)

Similar thing with the y- intercept. On the y-axis all the x's are zero, so you just substitute x by zero which gives you f(0)=-3(0+5)(0-11)=165 which means your function meets the y-axis at point C(0,165)

for concavity check function second order derivative  if it is positive then it is concave up othrerwise it is concave down.

dy/dx=18-6x

d2y/d2x=-6

so it is negative means it is concave down functon.


x-intercept (-5,0) and (11,0)

y-intercept (0,165)

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