<u>Answer</u>:
3y = 4(x - 1.5)²
<u>Step-by-step explanation:</u>
The equation of the parabola in the vertex form is:
y = a (x-h)² + k
Where: (h,k) the coordinates of the vertex & a is a multiplier
The parabola has a vertex at ( 1.5 , 0 )
So, h = 1.5 , k = 0
∴ y = a (x - 1.5)² + 0
∴ y = a (x - 1.5)²
The parabola passes through points ( 3 , 3 )
∴ 3 = a (3 - 1.5)²
∴ 1.5² a = 3 ⇒ a = 3/1.5² = 3/2.25 = 4/3
∴ y = (4/3) (x - 1.5)²
mukitbly both sides by 3
∴ 3y = 4(x - 1.5)²
So, the equation of a parabola that has a vertex at ( 1.5 , 0 ) and passes through points ( 3 , 3 ) is 3y = 4(x - 1.5)²
See the attached figure.
