301 MrG What's a Quadratic?

2475 days ago by MATH4R2013

#1a) (p185 #23) f(x)==-x^2-6*x find x-intercepts f(x)=-x^2-6*x solve(f(x),x) 
       
#1b) f(x)==-x^2-6*x find y-intercepts f(0) 
       
#1c) f(x)==-x^2-6*x find the axis of symmetry (-6+0)/2 
       
#1c)f(x)==-x^2-6*x find the axis of symmetry a=-1 b=-6 -b/(2*a) 
       
#1d) f(x)==-x^2-6*x find the turning point or max f(-3) 
       
#1d) graph f(x)==-x^2-6*x plot(f(x),-6,0) 
       
#2a) (p185 #61) A(x)=(200-x)*x, find the x-intercepts A(x)=(200-x)*x solve(A(x)==0,x) 
       
#2a) A(x)=(200-x)*x, find the max area show(expand(A(x))) a=-1 b=200 show(bool((0+200)/2==-b/(2*a))) show(-b/(2*a)) show(A(100)) plot(A(x),0,200) 
       




#3) (p185 #75) crude oil regression var('a,b,c') l=[[0,3.69],[1,2.93],[2,2.76],[3,2.40],[4,2.17],[5,2.34],[6,2.90]] f(x)=a*x^2+b*x+c q=find_fit(l,f,solution_dict=True) show(q[a]) show(q[b]) show(q[c]) show(f(a=q[a],b=q[b],c=q[b])) show(q[a]*7^2+q[b]*7+q[c]) points(l,color='blue')+plot(f(a=q[a],b=q[b],c=q[c]),(x,0,7),color='red') 
       





f(x)=q[a]*x^2+q[b]*x+q[c] show(f(x)) x1=solve(f(x)==3,x)[0].rhs().n() x2=solve(f(x)==3,x)[1].rhs().n() avg=(x1+x2)/2 show(x1) show(x2) show(avg) show(f(avg))