How do you find the vertex for y=2x2+11x−6?

2 Answers
Bill Jorgensen
Jun 9, 2018

y=2(x+114)2−652

Explanation:

Vertex form:

y=a(x+h)2+k

Vertex #=(-h,k)

To put this in vertex form you must complete the square on the x terms which is a pain because 11 is not divisible by 2:

first isolate the terms with x:

y=2x2+11x−6

y+6=2x2+11x

in the form ax2+bx+c to complete the square a must be 1 and:

c=(b2)2

a=2 so we have to factor it out:

y+6=2x2+11x

y+6=2(x2+112x)

now add c to both sides of the equation, we have to add 2c to the left side to account for the 2 we factored out:

y+6+2c=2(x2+112x+c)

now solve fo c:

c=(b2)2=(1122)2=12116

see what I mean about it being a pain, insert solution in function:

y+6+2(12116)=2(x2+112x+12116)

now complete the square:

y+6+532=2(x+1122)2

y+122+532=2(x+114)2

y+652=2(x+114)2

y=2(x+114)2−652

vertex =(−114,−652)

graph{2x^2 +11x-6 [-20.33, 25.28, -25.08, -2.28]}

Nghi N.
Jun 9, 2018

vertex (−114,−1698)

Explanation:

y(x)=2x2+11x−6
The x-coordinate of the vertex is given by the formula
x=−b2a=−114
The y-coordinate of vertex is the value of y(−114) -->
y(−114)=1218−1214−6=−1698
Vertex (−114,−1698)

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