#" "#

We are given the quadratic function in **Standard Form**:

#color(red)(y=f(x)=-3x^2+17x+2#

#color(blue)(y=f(x)=ax^2+bx+c#

**What is expected?**

We must convert to **Vertex Form**:

#color(blue)(y=f(x)=a(x-h)^2+k#

We have,

#y=f(x)=-3x^2+17x+2#

#color(green)("Step 1"#

Use **Completing the Square Method** to convert to **Vertex Form**:

#rArr (-3x^2+17x)+2#

#rArr -3[x^2-(17/3)x]+2#

#color(green)("Step 2"#

#rArr -3[x^2-(17/3)x+ square]+2#

In the #square# above, add #[(1/2)(17/3)]^2#

#rArr -3[x^2-(17/3)x+ [(1/2)(17/3)]^2]+2#

#rArr -3[x^2-(17/3)x+ (17/6)^2]+2#

#color(green)("Step 3"#

#rArr -3[x^2-(17/3)x+ (17/6)^2]+2- square#

Since we added #(17/6)^2# in the previous step, we must also subtract the same value.

#rArr -3[x^2-(17/3)x+ (17/6)^2]+2- (17/6)^2#

#color(green)("Step 4"#

On simplification, we get

#rArr -3[x^2-(17/3)x+ (17/6)^2]+(939/36)#

#y=f(x)= -3[x-17/6]^2+(939/36)#

Now, we have the required vertex form.

Hope this helps.