write 12X2-96X+197 in this form a(x+k)2+M

Question

Both number twos are squared. I know the answer is 12(x-4)2+5. the number 2 is squared. can you show me how to work out please .thank you

Answer 1

a(x+k)^2+m
=a(x^2+2kx+k^2)+m
=ax^2+2akx+ak^2+m

Compare to 12x^2-96x+197

12=a
-96=2ak
197=ak^2+m

a=12
k=-96/(24)=-4
m=197-ak^2=197-12(-4)^2=197-192=5

So 12x^2-96x+197 = 12(x-4)^2+5

Answer 2

Hi Roseland;

12X²-96X+197

The equation is in the form of...

ax²+bx+c

For such, the x-value of the vertex is -b/2a...

- {-96/[(2)(12)]}

--96/24

x=4

y=12X²-96X+197

y=[12(4²)]-[(96)(4)]+197

y=[(12)(16)]-[(96)(4)]+197

y=192-384+197

y=5

vertex is (4,5)

The parabolic equation which highlights the vertex is...

y=a(x-h)²+m

y=12(x-4)²+5

Let's check our results...

Let's FOIL (x-4)²...(x-4)(x-4)...

FIRST...(x)(x)=x²

OUTER...(x)(-4)=-4x

INNER...(-4)(x)=-4x

LAST...(-4)(-4)=16

x²-4x-4x+16

x²-8x+16

y=12(x²-8x+16)+5

y=12x²-96x+192+5

y=12x²-96x+197