Mathematics: ..vertex: (4, -1) f(3) = -6

She isn t correct. 43 is a 2-digit odd number but it isn t composite. It s a prime number....

..vertex: (4, -1) f(3) = -6 - id413610278541, HighSchool97654

quanntwann2873

16.03.2022

$\huge\boxed{f(x)=-5(x-4)^2-1=-5x^2+40x-81}$

Step-by-step explanation:

The vertex form of an equation of a parabola:

f(x)=a(x-h)^2+k

$(h;\ k)$ - vertex

We have

vertex $(4;\ -1)\to h=4;\ k=-1$

f(3)=-6

Therefore we have:

f(x)=a(x-4)^2+(-1)=a(x-4)^2-1

Substitute x=3 and f(3)=-6

$a(3-4)^2-1=-6\qquad|\text{add 1 to both sides}\\\\a(-1)^2=-6+1\\\\a(1)=-5\\\\a=-5$

Finally:

$f(x)=-5(x-4)^2-1=-5(x^2-2(x)(4)+4^2)-1\\\\=-5(x^2-8x+16)-1=-5x^2+(-5)(-8x)+(-5)(16)-1\\\\=-5x^2+40x-80-1=-5x^2+40x-81$

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