How do you write 0=2X2+13X−1 in vertex form?

2 Answers
Nghi N
Aug 15, 2017

f(x) = 2(x + 13/4)^2 - 22

Explanation:

f(x)=2x2+13x−1
x- coordinate of vertex:
x=−b2a=−134
y-coordinate of vertex:
f(−134)=216916−13(134)−1=33616−1694−1=35216=−22
Vertex form:
f(x)=2(x+134)2−22

iceman
Aug 15, 2017

2(x+134)2−1778

Explanation:

2x2+13x−1=0
To convert standard from of the quadratic equation into the vertex form complete the square:
2(x2+(132)x)−1=0
2[x2+(132)x+(134)2]−1−2(134)2=0
2(x+134)2−(1+1698)=0
2(x+134)2−1778=0 => in the vertex form of y=a(x−h)2+k where: (h,k) is the vertex.
Thus in this case:
#(-13/4, -177/8) is the vertex

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