Question

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

Answer 1

Answer:

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

Step-by-step 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 ;

$\longrightarrow \boxed{h =\dfrac{-b}{2a}}$

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

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;

$\longrightarrow h =\dfrac{-b}{2a}$

$\longrightarrow h =\dfrac{-(12)}{2(3)}$

$\longrightarrow h =\dfrac{12}{6}$

$\longrightarrow h = 2$

And ,

$\longrightarrow k =\dfrac{-D}{4a}$

$\longrightarrow k =\dfrac{-(b^2-4ac)}{4a}$

$\longrightarrow k =\dfrac{-\{(-12)^2-4(3)(2)\}}{4(3)}$

$\longrightarrow k =\dfrac{-(144-24)}{12}$

$\longrightarrow k =\dfrac{-120}{12}$

$\longrightarrow k = -10$

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 !