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A portion of the graph of a quadratic function $f(x)$ is shown below.  Let $g(x)=-f(x)$ and $h(x)=f(-x)$. If $a$ is the number of points where the graphs of $y=f(x)$ and $y=g(x)$ intersect, and $b$ is the number of points where the graphs of $y=f(x)$ and $y=h(x)$ intersect, then what is $10a+b$?

Guest Jul 24, 2018
 #1
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g(x) = -f(x)  will "flip" the graph of f(x) over the  x axis.....it will intersect with f(x)  in two places - at the points where f(x)  intersects the  x axis...so  "a"  = 2

 

h(x)  = f(-x) will  "flip" the graph of f(x) across the  y axis..it wil intersect with  f(x)  in one place - at the point where f(x) intersects the y axis...so...."b" = 1

 

So  10a + b  =   10(2) + 1  =   20 + 1   = 21

 

 

cool cool cool

CPhill  Jul 24, 2018

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