NARRATOR: Exercise three.
A parabola has vertex (1, 3) and passes through the point (3, 11).
Find its equation.
We know that an equation given in turning point form -
that is in the form y = a(x – h) all squared plus k -
has a vertex at (h, k).
So in this case, with the vertex at (1, 3),
the equation will be of the form y = a(x – 1) all squared, + 3.
So with the equation in this form,
the point (3, 11) can be used to calculate a.
So we substitute the point (3, 11) in -
that is, when x = 3, y = 11.
In simplifying and solving for a, we find that a is equal to 2.
So therefore the equation of the parabola
which has a vertex at (1, 3) and passes through the point (3, 11)
is y = 2(x-1) all squared, + 3.