Mathematics: Use the graph to write an equation for the parabola,

Use the graph to write an equation for the parabola,

kevenluna10oytivm

12.01.2022

$\large\boxed{y=\dfrac{1}{3}x^2=\dfrac{x^2}{3}}$

Step-by-step explanation:

The vertex form of na equation of a parabola:

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

(h, k) - vertex

We have a vertex in (0, 0). Therefore h = 0, k = 0.

The equation has form:

y=a(x-0)^2+0=ax^2

From the graph we have the point (3, 3).

Put the coordinates of the point to the equation:

3=a(3^2)

3=9a divide both sides by 9

$\dfrac{3}{9}=\dfrac{9a}{9}\\\\\dfrac{3:3}{9:3}=a\to a=\dfrac{1}{3}$

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