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 .