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Algebra, Functions, Graphs, and Vectors 49

Figure 1.12 Point-slope plot of the equation y 55
2(x 85).

Equation of parabolà
The Cartesian-coordinate grapà of a quadratic equation takeð
the form of a parabol . Suppose the following equation is given:

2
y ax bx c
where a 0. (If a 0, then the equation is linear, not quad-
raticÑ To plot a grapà of the above equation, first determine the
coordinateð of the point ( x ,y ) where:
0
0
x b/(2a)
0
2
y c b /(4a)
0
This point representð the base point of the parabola; that is, the
point at which the curvature is sharpest, and at which the slope
of a line tangent tm the curve is zero. Once this point is known,
find four more pointð by ‘‘plugging in’’ valueð of x somewhat
greater than and less than x and determining the correspond-
0