What is the vertex form of y=x2+5x+6?

1 Answer
Meave60
Jul 24, 2017

Vertex form is (x+52)2−14.

Explanation:

Vertex from Standard Form

y=x2+5x+6 is the standard form for a quadratic equation, ax2+bx+6, where a=1, b=5, and c=6.

The vertex form is a(x−h)2+k, and the vertex is (h,k).

In the standard form, h=−b2a, and k=f(h).

Solve for h and k.

h=−52⋅1

h=−52

Now plug in −52 for x in the standard form to find k.

f(h)=k=(−52)2+(5×−52)+6

Solve.

f(h)=k=254−252+6

The LCD is 4.

Multiply each fraction by an equivalent fraction to make all of the denominators 4. Reminder: 6=61

f(h)=k=254−(252×22)+(61×44)

Simplify.

f(h)=k=254−504+244

Simplify.

f(h)=k=−14

Vertex (−52,−12)

Vertex form: a(x−h)2+k

1(x+52)2−14

(x+52)2−14

Related questions
See all questions in Vertex Form of a Quadratic Equation
Impact of this question
11261 views around the world
You can reuse this answer
Creative Commons License