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**+1 **

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

CPhill
Jul 24, 2018