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Wednesday, 9 December 2015

Quadratic function problem - maximum height - frogs leap


SOLUTION ==========================
h(x)=\displaystyle -{1\over 3}x^2+{4\over 3}x+4 

(a) We need to know where the maximum occurs, this will be on the axis of symmetry. 
You may know the formula x={-b\over 2a}
for the axis of symmetry, which gives 

x={-(4/3)\over 2(-1/3)}=2
 


[you could also see this by factorising h(x)=-1/3(x^2-4x-12)=-1/3(x+2)(x-6)
and so the max occurs half way between the x-intercepts which are x=-2, x=6, so max occurs at x =(-2+6)/2=2 as before.] 


So the max occurs when x=2, and since the frog starts at x=0, then it reached the maximum height after 2 ft. 

(b) When x=2,  
h(2)=-1/3 (2)^2+4/3(2)+4
= -4/3+8/3+4
=5 1/3 or {16\over 3} ft 

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