The figure above shows the graphs of f(x) and g(x), where f(x)=-(x-1)^2+6 and g(x)=(x-3)^2+2. If h(x)=mx+b, where m and b are constants, and f(x)=g(x)=h(x) for exactly two values of x, what is the value of b ?



Comments (2)

That too much work! you only have on average less than 2 minutes for each problem
Use the slope-a -dope method
You see that mx +b formula and you take a piece of paper and line up the y intercept through the two points because when you set x to 0 that will give you the y intercept which is b. you see the line crosses the y axis at 8 when x is set to zero. (bi is always the y intercept because when that x neutralizes the m value to zero all you are left with is the y value where the corresponding x is at zero.) B is like a cockroach no matter what happens to the input or x such as atomic bombs, flood, insecticides, it always remains.

This time I knew that b was simply the Y intercept ( when x is zero what is y) so I did the paper trick and it worked.– super fast but I checked the math just in case

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