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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 $10a+b$?

 Sep 20, 2022
 #1
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10a + b = 43.

 Sep 20, 2022
 #2
avatar+502 
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g(x) will reflect f(x) across the x axis, intersecting with f(x) at the 2 roots.

h(x) will reflect f(x) across the y axis, intersecting with f(x) at the y interception of f(x).

to see why g(x) and h(x) are reflections of f(x) across the x and y axis respectively, try seeing what happens when you change the input for the 2 functions.

 Sep 20, 2022

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