Write the equation of the parabola that has the vertex at point (1.5,0) and passes through the point (3,3).

Answer:

3y = 4(x - 1.5)²

Step-by-step explanation:

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.

333333333333333333333333333333

step-by-step explanation:

a_n = a_1 + (n - 1)d

the first term is 6.

the common difference d = ?

when you find d, replace n with 7 and d with the common difference to find your answer.