What is the vertex form of #y=3x^2 - 4x +17?

1 Answer

The Vertex Form

color(red)((x-2/3)^2=1/3(y-47/3))

Explanation:

Start from the given

y=3x^2-4x+17

from the numerical coefficients
a=3 and b=-4 and c=17

The vertex can be computed

h=(-b)/(2a)
h=(-(-4))/(2*3)

h=2/3

for the k
k=c-b^2/(4a)

k=17-(-4)^2/(4*3)

k=47/3

p=1/(4a)=1/(4*3)=1/12

The vertex form

(x-h)^2=+4p(y-k)

(x-3/2)^2=4(1/12)(y-47/3)

(x-3/2)^2=1/3(y-47/3)

By completing the square method

y=3x^2-4x+17
y=3(x^2-4/3x)+17

y=3(x^2-4/3x+4/9-4/9)+17

y=3((x^2-4/3x+4/9)-4/9)+17

y=3((x-2/3)^2-4/9)+17

y=3(x-2/3)^2-4/3+17

y=3(x-2/3)^2+47/3

y-47/3=3(x-2/3)^2

1/3(y-47/3)=(x-2/3)^2

The Vertex Form

color(red)((x-2/3)^2=1/3(y-47/3))

God bless....I hope the explanation is useful.