The graph of which of the following equations contains the points (2,3) and (3,2)
1 answer:
Answer:
Step-by-step explanation:
The graph of the equation that will contain the points (2, 3) and (3, 2) is the graph that has a slope value that is equivalent to the slope value of the line running through the two points.
Slope of the line running through (2, 3) and (3, 2):
.
Slope (m) = -1.
The equation, , is given in the slope-intercept form, which means it has a slope value of -1. I.e. the term "-x" is equivalent to -1x. So therefore, the graph of the equation that contains the points (2, 3) and (3, 2) is
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so draw a graph starting from bottom left and going through those points and ending at bottom right
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so it goes through the y axis (up and down line) at y=-6
now find the x intercepts, or where y=0
factoring we get P(x)=-1(x+2)(x+1)(x-1)(x-3)
so it goes through the y axis at x=-2, x=-1, x=1, and x=3
put those points
now, the function is 4th degree and the leading coefient is negative, so it starts from bottom left and ends at bottom right
so draw a graph starting from bottom left and going through those points and ending at bottom right
since they are all odd multiplicities, the graph goes through the points to the other side of x axis instead of bouncing off
see graph included (hand drawn)