Question

Use the information provided to write the equation of the parabola in vertex form. y=3x^2-12x+2

Answer 1

`y = 3(x-2)^2-10`

Explanation:

We would like to write the given equation of parabola in vertex form .

`\longrightarrow y = 3x^2-12x + 2`

As we know that the vertex form of parabola is ,

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

where ,

• 
  `(x,y)` is a point on parabola .
• 
  `(h,k)` is the vertex of parabola .

Method :- By using the formula :-

For a equation in Standard form ( y = ax² + bx + c ) , we can find h and k , by using ;

`\longrightarrow \boxed{h =(-b)/(2a)}\\`

`\longrightarrow \boxed{ k =(-D)/(4a) =(-(b^2-4ac))/(4a)}`

The given equation is , y = 3x² -12x + 2 , on comparing to Standard form , we have ;

`\longrightarrow a = 3 \quad , \quad b = (-12)\quad,\quad c = 2`

On substituting the respective values, we have;

`\longrightarrow h =(-b)/(2a)\\`

`\longrightarrow h =(-(12))/(2(3))\\`

`\longrightarrow h =(12)/(6)\\`

`\longrightarrow h = 2`

And ,

`\longrightarrow k =(-D)/(4a)\\`

`\longrightarrow k =(-(b^2-4ac))/(4a)\\`

`\longrightarrow k =\frac{-\{(-12)^2-4(3)(2)\}}{4(3)}\\`

`\longrightarrow k =(-(144-24))/(12)\\`

`\longrightarrow k =(-120)/(12)\\`

`\longrightarrow k = -10`

Now finally substitute the values of h and k in the vertex form ,

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

`\longrightarrow \underline{\underline{y = 3(x-2)^2-10}}`

And we are done !