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PART A
The equation of the parabola in vertex form is given by the formula,
where
is the vertex of the parabola.
We substitute these values to obtain,
The point, (3,6) lies on the parabola.
It must therefore satisfy its equation.
Hence the equation of the parabola in vertex form is
PART B
To obtain the equation of the parabola in standard form, we expand the vertex form of the equation.
This implies that
We expand to obtain,
This will give us,
This equation is now in the form,
where
This is the standard form
The equation of the parabola in vertex form is given by the formula,
where
is the vertex of the parabola.
We substitute these values to obtain,
The point, (3,6) lies on the parabola.
It must therefore satisfy its equation.
Hence the equation of the parabola in vertex form is
PART B
To obtain the equation of the parabola in standard form, we expand the vertex form of the equation.
This implies that
We expand to obtain,
This will give us,
This equation is now in the form,
where
This is the standard form
The common rule is (x - 1, y + 3) can be used to describe the translation.
Step-by-step explanation:
Step 1:
The point J (-3, -4) becomes (-4, -1).
In order to write the rule for translation from J to , we subtract the x coordinate of J from
and subtract the y coordinate of J from
.
The x coordinate
The y coordinate
Step 2:
So from the calculations, we get that the x coordinate is subtracted by 1 i.e. and the y coordinate is increased by 3 i.e.
.
So the common rule is (x - 1, y + 3).