what is the vertex of the quadratic function f(x)=2x^2+4x+3 a.) (-1,1) b.) (0,3) c.) (1,-1) d.) (3,0)
Mathematics · Middle School · Thu Feb 04 2021
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according to the question, f(x)=2x^2+4x+3 is a quadratic function then its vertex form is:-
f(x) = a(x - h)2 + k
where points (h, k) are vertex of this equation now, convert this equation in vertex form:-
f(x)=2x^2+4x+2+1 (breakdown 3 into 2 and 1)
f(x) = 2(x^2 + 2x + 1) + 1 (common 2 from 2x^2+4x+2)
f(x) = 2(x + 1)(x + 1) + 1 ((x+1)^2=x^2+2x+1)
f(x) = 2(x + 1)^2 + 1
f(x)=2(x-(-1))^2+1
h = -1
k = 1
vertex of this quadratic equation (h,k) is (-1,1)