Question

Write the equation of the parabola that has the vertex at point (−0.5, 2.3) and passes through the point (5, 2.75).

Answer 1

The vertex form of equation of a parabola:

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

(h, k) - vertex

We have the vertex (-0.5, 2.3). Therefore h = -0.5 and k = 2.3.

Substitute:

`y=a(x-(-0.5))^2+2.3\\\\y=a(x+0.5)^2+2.3`

We have the point (5, 2.75). Put the coordinstes of the point to the equation of parabola:

`2.75=a(5+0.5)^2+2.3\qquad\text{subtract 2.3 from both sides}\\\\0.45=a(5.5)^2\\\\0.45=30.25a\qquad\text{divide both sides by 30.25}\\\\a=(0.45)/(30.25)\\\\a=(45:5)/(3025:5)\\\\a=(9)/(605)`

`Answer:\ \boxed{y=(9)/(605)(x+0.5)^2+2.3}`