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:

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

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