What is the equation of a parabola with a vertex at the origin and the graph containing (-3,3)?

Question

asked Apr 9, 2019 155k views

1 Answer

Joakim Johansson · Answer 1 · 2019-04-16T18:13:48+0000

Answer:

$y=\frac13x^2$

Explanation:

Each parabola
y=ax^2 has a vertex at the origin.

Point (-3,3) means that x=-3, y=3 substitute it to the equation
y=ax^2 and calculate "a".

$3=a\cdot (-3)^2\\ 3=a\cdot 9\\ 3=9a\\ 9a=3\ \ \ \ |:9\\ a=\frac39\\ a=\frac13$

Put
$a=\frac13$ to the equation
y=ax^2

$y=\frac13x^2$