What is the equation of the line through 12 and 3 1 2 What i

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

Solution

1) equation of the line through (1,2) and (3, -1)

slope = (-1 -2)/(3-1) = -3/2

y = mx +c---> y = -3x/2 +c

plug any point to solve for c: (1.2)

2 = -3/2 +c---> c= 2+3/2 =7/2

y = -3x/2 +7/2

2y +3x=7

2) f(x) = x^2 -6x +3

vertex for quadratice function :x=-b/2a = -(-6)/(2*1) = 3

f(3) = 3^2 -6*3 +3 = 9-18+3 = -6

Vertex =(3, -6)