Answer:
y=x^2 -5x+4
Step-by-step explanation:
F(x)= -x+1
G(x)-x+4
(-x+1)(-x+4) = x^2 -4x-1x+4 = x^2-5x+4
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Explanation:
The f(x) function goes through (0,1) and (1,0). It's slope is
m = (y2-y1)/(x2-x1)
m = (0-1)/(1-0)
m = -1
The y intercept is b = 1 because this is where the blue line crosses the y axis.
We go from y = mx+b to y = -1x+1, or simply y = -x+1.
So f(x) = -x+1
Through similar steps, you should find that g(x) = -x+4
Both f(x) and g(x) have the same slope, which makes them parallel lines.
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Once we know what f(x) and g(x) are, we multiply them out like so:
f(x) * g(x) = ( f(x) ) * ( g(x) )
f(x) * g(x) = ( -x+1 ) * ( -x+4 )
f(x) * g(x) = w(-x+4) ..... let w = -x+1
f(x) * g(x) = -xw + 4w ... distribute
f(x) * g(x) = -x( w ) + 4( w )
f(x) * g(x) = -x( -x+1 ) + 4( -x+1 ) ... plug in w = -x+1
f(x) * g(x) = x^2 - x - 4x + 4 ... distribute twice more
f(x) * g(x) = x^2 - 5x + 4
You could use the FOIL rule or box method as alternative routes to get this answer. I prefer the box method because the FOIL rule is only limited to multiplying binomials, while the box method allows you to multiply two polynomials of any length.
