The equation is .
Let .
,
Standard form equation .
Compare the above two equations,
Find the equation of the axis of symmetry:
\Formula for the equation of the axis of symmetry: .
(Substitute
)
(Product of two same signs is positive)
(Multiply:
)
(Cancel common terms)
The equation for the axis of symmetry is .
Find vertex:
\and determine whether it is a maximum or minimum.
\ (Original equation)
(Substitute
)
(Evaluate powers:
)
(Apply multiplicitive identity property:
)
(Apply multiplicitive identity property:
)
. (Subtract:
)
The vertex lies at . Because a is positive the graph opens up,and the vertex is a minimum.
(Original equation)
(Substitute
)
(Evaluate powers:
)
(Apply zero product property:
)
(Subtract:
)
The y-intercept is .
iThe axis of symmetry divides the parabola into two equal parts.So if there is a point on one side,there is a corresponding point on the other side that is the same distance from the axis of symmetry and has the same y-value.
\Connect the points with a smooth curve.
\The graph of the equation is
\