What is the x-coordinate of the vertex y=x^{2}+2x+1?

Lainey Goodwin

Lainey Goodwin

Answered question

2022-01-20

What is the x-coordinate of the vertex
y=x2+2x+1?

Answer & Explanation

pacetfv

pacetfv

Beginner2022-01-21Added 9 answers

Step 1
It is always helpful to know how the graph of a function y=F(x) is transformed if we switch to a function
y=a×F(x+b)+c
This transformation of the graph of y=F(x) can be represented in three steps:
a) stretching along Y-axis by a factor of a getting y=a×F(x)
b) shifting to the left by b getting y=a×F(x+b)
c) shifting upwards by c getting y=a×F(x+b)+c
To find a vertex of a parabola using this methodology, it is sufficient to transform the equation into a full square form that looks like
y=a×(x+b)2+c
Then we can say that this parabola is the result of a shift upwards by c (if c<0, it's actually downward by |c|) of a parabola with an equation
y=a×(x+b)2
That last one is a result of shifting to the left by b (if b<0, it's actually to the right by |b|) of a parabola with an equation
y=a×x2
Since the parabola y=a×x2 has a vertex at (0, 0), the parabola y=a×(x+b)2 has a vertex at (b, 0)
Then the parabola y=a×(x+b)2+c has a vertex at (b, c)
Let's apply it to our case:
y=x2+2x+1=(x+1)2+0
Hence, the vertex if this parabola is at (1, 0).

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