Question

Question: Write the equation of a parabola having the vertex (1, −2) and containing the point (3, 6) in vertex form. Then, rewrite the equation in standard form.

[Hint: Vertex form: y - k = a(x - h)2]

Answer 1

`y+2=2(x-1)^(2)` -----> vertex form

`y=2x^(2)-4x` -----> standard form

Explanation:

we know that

The equation of a vertical parabola in vertex form is equal to

`y-k=a(x-h)^(2)`

where

(h,k) is the vertex of the parabola

In this problem we have

`(h,k)=(1,-2)`

`Point(3,6)`

substitute the values and solve for a

`6-(-2)=a(3-1)^(2)`

`8=a(2)^(2)`

`8=a(4)`

`a=2`

the equation in vertex form is equal to

`y+2=2(x-1)^(2)`

Find the equation of the parabola in standard form

we know that

the equation of the parabola in standard form is equal to

`y=ax^(2)+bx+c`

we have

`y+2=2(x-1)^(2)`

convert to standard form

`y+2=2(x^(2)-2x+1)\\ \\y+2= 2x^(2)-4x+2\\ \\y=2x^(2)-4x+2-2\\ \\y=2x^(2)-4x`