[tex]\boxed{y=\frac{4}{3}(x-1.5)^2}[/tex]
Explanation:
The vertex form of the equation of a parabola is given by:
[tex]y=a(x-h)^2+k \\ \\ \\ Where: \\ \\ (h,k):Vertex \\ \\ a:Leading \ coefficient[/tex]
From the statement above we know that the vertex is:
[tex](h,k)=(1.5,0)[/tex]
Moreover, we have that the parabola passes through:
[tex](3,3)[/tex]
So, substituting all these values into the equation we get:
[tex]3=a(3-1.5)^2+0 \\ \\ \frac{9}{4}a=3 \\ \\ a=\frac{4}{3}[/tex]
Finally, our equation becomes:
[tex]\boxed{y=\frac{4}{3}(x-1.5)^2}[/tex]
Learn more:
Parabola: https://brainly.com/question/1469367
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