SOLUTION: A Parabola with the equation {{{y=ax^2}}} passes through three vertices of a square. if the area of the square = 18, find the value of {{{a}}} in {{{y=ax^2}}}.
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-> SOLUTION: A Parabola with the equation {{{y=ax^2}}} passes through three vertices of a square. if the area of the square = 18, find the value of {{{a}}} in {{{y=ax^2}}}.
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Question 173551: A Parabola with the equation passes through three vertices of a square. if the area of the square = 18, find the value of in . Answer by Edwin McCravy(20060) (Show Source):
You can put this solution on YOUR website! A Parabola with the equation passes through three vertices of a square. if the area of the square = 18, find the value of in .
The formula for the area of a square, where
is the length of each side is
Substitute 18 for A
Take square roots of both sides
So each side is
We draw the square:
Let's draw a diagonal:
Use the Pythagorean theorem to find the length
of the diagonal:
Taking square roots:
Now since the diagonal is 6, let's tilt the square
45° and put the diagonal along the y-axis with a
corner at the origin, like this:
We draw the other diagonal:
Since the vertical diagonal is 6 units,
so is the horizontal diagonal, so
the two vertices at the end of the
horizontal diagonal are
and
We put the coordinates at these corners:
Now we can roughly sketch in the parabola
we are looking for:
We put the coordinates at these corners:
Since the parabola has the form ,
and goes through ,
we substitute and
The value of is therefore and
the equation of the parabola is
Edwin