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

User Flappix
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1 Answer

7 votes
7 votes

Answer:


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 !

Use the information provided to write the equation of the parabola in vertex form-example-1
User Brunorey
by
2.5k points
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