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Answer: y = 5(x - 3)² - 2

Step-by-step explanation:

Vertex form: y = a(x - h)² + k  where (h,k) is the vertex and "a" is the vertical stretch

Given (h, k) = (3, -2) and (x, y) = (2, 3), we can find the a-value.

3 = a(2 - 3)² - 2

3 = a(1) - 2

+2          +2

5 = a

Next, input the vertex and the a-value into the vertex equation.

y = 5(x - 3)² - 2

Here,

vertex=(h,k)=(3,-2)

point=(x,y)=(2,3)

So,

[tex]\boxed{Vertical~ form=y=a(x-h)^2+k }[/tex]

in this ,a is the vertical stretched and (h,k)Are the vertex,.

So,value of a =

[tex]\tt{3=a(2-3)^2-2 }[/tex]

[tex]\tt{ 3=a×(-1)^2-2 }[/tex]

[tex]\tt{ 3=a×1-2 }[/tex]

[tex]\tt{ 3=a-2 }[/tex]

[tex]\tt{ a=3+2 }[/tex]

[tex]\tt{a=5 }[/tex]

So According to the question,

equation of the parabola in vertex form=

[tex]\bold{ y=5(x-3)^2-2 }[/tex]

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