quadratic function

a)x=-1

b)Put (x,y)=(0,-8)
-8=(0+1)^2+k
k=-9
V is the intersect of x=-1 and y=(x+1)^2-9
So that y=(-1+1)^2-9
y=0-9
y=-9
therefore V=(-1,-9)

ci)Now,use the area 公式 of paralleglogram
height乘base/2 其實係三角形公式 當底係PR
Q point is a moving point on the graph
so function A(x)=PR乘(-2y/2)[因為我想要個高係正數]
so function A(x)=PR乘(-y)
so function A(x)=PR乘{-[(x+1)^2-9]}
咁面積要正 PR本身係正 所以-y要係正
-[(x+1)^2-9]>=0
(x+1)^2-9<=0[a^2-b^2=(a+b)(a-b)]
(x+4)(x-2)<=0
-4<x<2
so that the domain of the function A is -4<x<2

cii)先搵左PR先
因為最大值係底高都要最大,RP就係最大底
Put y=0 to y=(x+1)^2-9
0=(x+1)^2-9
0=(x+4)(x-2)[a^2-b^2=(a+b)(a-b)]
x=2or-4
So PR=2-(-4)=6
A(x)=6乘{-[(x+1)^2-9]}
Now,當y=(x+1)^2-9最小,-y=高={-[(x+1)^2-9]}最大
(x+1)^2-9最小就係v當點
so 最大值of A(x)=6乘9
=54
So the greatest possible area of the parallelogram PQRS is 54 square units.
如果喜歡
可以先寫出A(x)=6乘{-[(x+1)^2-9]}
再用completing square method
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