A transformation that leaves the graph unchanged is regarded as asymmetry of a function. In this the value of b is [tex]-\frac{9}{5}[/tex] and zeros are 8, -2.
Function:
[tex]F(x)=x^2+bx-16[/tex]
Part a)
when x=5
b=?
Part b)
b=-6
zero=?
The calculation for part a:
[tex]F(x)=x^2+bx-16[/tex]
x=5
[tex]\to F(5)=5^2+b\times 5-16\\\\\to 25+5b-16=0\\\\\to 9+5b=0\\\\\to 5b=-9\\\\\to b=-\frac{9}{5}[/tex]
The calculation for part b:
[tex]F(x)=x^2+bx-16[/tex]
b= -6
[tex]\to F(x)=x^2+ (-6)\times x-16\\\\\to F(x)=x^2-6x-16\\\\[/tex]
[tex]\to x^2-6x-16=0\\\\\to x^2-(8x-2x)-16=0\\\\\to x^2-8x+2x-16=0\\\\\to x(x-8)+2(x-8)=0\\\\\to (x-8) (x+2)=0\\\\\to x-8=0\ \ \ \ \ \ \ \ \ \ \ or \ \ \ \ \ \ \ x+2=0\\\\\to x=8\ \ \ \ \ \ \ \ \ \ \ or \ \ \ \ \ \ \ x=-2\\\\[/tex]
So, the value of b is [tex]-\frac{9}{5}[/tex] and zeros are 8, -2.
Find out more about the symmetry here:
brainly.com/question/15970176
