Question

Write the equation of the parabola that passes through the point (2, -2) with a vertex at (0.5, 0.25).(7 points)
y=a(x−h)2+k

=a
(
-
)2 +

=a
(
)2

a=−1

y=

Answer 1

Using vertex form y = a(x − h)^2 + k with (h,k) = (0.5, 0.25):

-2 = a(2 − 0.5)^2 + 0.25 = a(1.5)^2 + 0.25 = 2.25a + 0.25
=> 2.25a = −2.25 => a = −1.

So y = −(x − 0.5)^2 + 0.25, which simplifies to y = −x^2 + x.