Question

The parabola starts at left parenthesis 1 comma 0 right parenthesis and passes through left parenthesis 2 comma 5 right parenthesis to its vertex at left parenthesis 5 comma 10 right parenthesis. It continues through left parenthesis 8 comma 5 right parenthesis and ends at left parenthesis 9 comma 0 right parenthesis. All values are approximate.

The graph shows the trajectory of a firework. Which equation in vertex form matches this graph?

(1 point)

y=−1/2(x−5)2+10


y=1/2(x−5)2+10


y=−1/2(x−5)2−10


y=1/2(x+5)2+10

Answer 1

y = −1/2(x − 5)^2 + 10

Reason: The vertex is (5, 10) so the form is y = a(x − 5)^2 + 10. The parabola opens downward, so a < 0. The only choice with those features is y = −1/2(x − 5)^2 + 10 (and its values match the given points approximately).