Question

Write the equation of the parabola in vertex form.

vertex (3, -2), point (2, 3)

Answer 1

Here,

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

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

So,

`\boxed{Vertical~ form=y=a(x-h)^2+k }`

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

So,value of a =

`\tt{3=a(2-3)^2-2 }`

`\tt{ 3=a×(-1)^2-2 }`

`\tt{ 3=a×1-2 }`

`\tt{ 3=a-2 }`

`\tt{ a=3+2 }`

`\tt{a=5 }`

So According to the question,

equation of the parabola in vertex form=

`\bold{ y=5(x-3)^2-2 }`

Answer 2

Answer: y = 5(x - 3)² - 2

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