Observe the graph:
\The coordinate points are
and
.
The general equation of a quadratic function is
,
.
The graph passes through
.
Find
.
(Quadratic function)
(Substitute
)
(Simplify)
Rewrite the quadratic function is
.
Find
.
The graph passes through the point
and
.
Case (i):
\
(Quadratic function)
(Substitute
)
(Simplify)
Case (ii):
\
(Quadratic function)
(Substitute
)
(Simplify)
Add simplified case (i) and case (ii) equations and find
value.

(Divide each side by
)
(Cancel common terms)
Find
.
(Substitute )
(Multiply)
(Add
to each side)
(Divide each side by
)
(Cancel common terms)
Find the quadratic equation.
\
(Quadratic function)
(Substitute
,
and
)
Consider the test value from the graph
.
