Question

Write the equation of a parabola that has a vertex of (-2,5.5) and passes through the point (-2.5,2.5).

Answer 1

The equation of a parabola that has a vertex of (-2, 5.5) and passes through the point (-2.5, 2.5) is  $y=-12(x+2)^2+5.5$

The vertex form of the equation of a parabola is:

$y=a(x-h)^2+k$

where (h, k) is the vertex of the parabola

(x, y) is the point that the parabola passes through

The vertex, (h, k) = (-2, 5.5)

The point, (x, y) = (-2.5, 2.5)

Substitute h = -2, k = 5.5, x = -2.5, and y = 2.5 into the equation to solve for a.

$2.5=a(-2.5-(-2))^2+5.5\\\\2.5=a(-2.5+2)^2+5.5\\\\2.5-5.5=a(-2.5+2)^2\\\\-3=a(-0.5)^2\\\\-3=0.25a\\\\a = \frac{-3}{0.25} \\\\a = -12$

Therefore, the equation of the parabola is:

$y=-12(x-(-2))^2+5.5\\\\y=-12(x+2)^2+5.5$

Learn more here: brainly.com/question/25667732