Graph f(x)=1/2x^2
Problem
Solution
Identify the function type as a quadratic function in the form
ƒ(x)=a*x2 which represents a parabola opening upward with its vertex at the origin(0,0) Determine the vertical stretch or compression factor, where
a=1/2 indicates the parabola is wider than the parent functiony=x2 Calculate several points to plot by substituting
x values into the function.Evaluate for
x=2 ƒ(2)=1/2*(2)2=2 giving the point(2,2) Evaluate for
x=−2 ƒ*(−2)=1/2*(−2)2=2 giving the point(−2,2) Evaluate for
x=4 ƒ(4)=1/2*(4)2=8 giving the point(4,8) Sketch the curve through the points
(0,0) (±2,2) and(±4,8) to form a smooth, symmetric U-shaped graph.
Final Answer
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