find expressions for the quadratic functions whose graphs are shown. f(x)=? g(x)=? 12110601361.jpg

banganX

banganX

Answered question

2021-06-04

find expressions for the quadratic functions whose graphs are shown.
f(x)=?
g(x)=?

Answer & Explanation

lamusesamuset

lamusesamuset

Skilled2021-06-05Added 93 answers

f(x)=a(xh)2+k vertex form
vertex (h,k)=(6,0)
so, f(x)=a(x6)2+0
f(x)=a(x6)2
passes through (7,2)
so, 2=a(76)2
2=a(1)a=2
Hence, f(x)=2(x6)2
*let g(x)=ax2+bx+c standard form
y intercept is 1 , so c=1
g(x)=ax2+bx+1
passes through (-4,11)
so, 11=a(4)2+b(4)+1
10=16a-4b
5=8a-2b
passes through (1,-6,5)
so,6,5=a(1)2+b(1)+1
-7,5=a+b
-15=2a+2b
So,
2a+2b=-15
8a-2b=5
10a=-10
a=-1
a+b=-7,5
-1+b=-7,5
b=-6,5
Hence,
g(x)=1x265x+1

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