1. What is the equation of the line through (1,2) and (3, -1)?
2. What is the vertex of f(x) = x2 – 6x + 3?
3. Using points, straight lines, and possibly the curve of a parabola, construct a piecewise function whose graph looks like a smiling face.
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1. What is the equation of the line through (1,2) and (3, -1)?
m = ( 2 - (-1) ) / (1 - 3) = 3/-2 = -3/2
y = -3/2*x + b
use (1,2) in this equation:
2 = -3/2*1 + b
b = 2 + 3/2 = 7/2
therefore, we get the equation:
y = -3/2*x + 7/2
2. What is the vertex of f(x) = x2 – 6x + 3?
f(x) = x^2 - 6x + (-3)^2 - (-3)^2 + 3
= (x - 3)^2 - 9 + 3
= (x - 3)^2 - 6
therefore, we can get vertex (3, -6)
3.




The graph of the f(x):