What is the vertex form of y=3x^2+2x-8 ?

1 Answer
Oct 7, 2017

y=3(x+0.bar(3))^2-8.bar(3)

Explanation:

Vertex form is written:

y=a(x-h)^2+k

Where (h,k) is the vertex.

Currently the equation is in standard form, or:

y=ax^2+bx+c

Where (-b/(2a),f(-b/(2a))) is the vertex.

Let’s find the vertex of your equation:

a=3 and b=2

So,

-b/(2a)=-2/(2*3)=-2/6=-1/3

Thus h=-1/3=-0.bar(3)

f(-1/3)=3(-1/3)^2+2(-1/3)-8
f(-1/3)=3(1/9)-2/3-8
f(-1/3)=1/3-2/3-8=-8.bar(3)

Thus k=-8.bar(3)

We already know that a=3, so our equation in vertex form is:

y=3(x-(-0.bar(3)))^2+(-8.bar(3))

y=3(x+0.bar(3))^2-8.bar(3)