Question

What is the equation of the following graph in vertex form?

Answer 1

y = (x − 2)2 + 1
y = (x − 1)2 + 2
y = (x + 2)2 + 1
y = (x + 2)2 − 1

Answer 2

@.Sam.

Answer 3

You have a vertex of (2,1), point of (0,5) so, using \(x=-\frac{b}{2a}\)
\[2=-\frac{b}{2a} \\ \\ b=-4a\]
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From the equation \(y=ax^2+bx+c\), pick a point, say \((2,1)\)
\[1=a(2)^2+(-4a)(2)+c \\ \\ \]
Since \((0,5)\) results in c=5,
\[1=a(2)^2+(-4a)(2)+5 \\ \\ \]
\[a=1\]
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Plug the 'a' in b=-4a you'll get b=-4, so
\[y=x^2-4x+5\]

Answer 4

Now just left with completing the square

Answer 5

Can you do it?

Answer 6

im not sure how to do it

Answer 7

Take the half of the coefficient of 'x', then square it, then subtract,
\[y=x^2-4x+5 \\ \\ y=(x^2-4x+4)+5-4\]
\[y=(x^2-4x+4)+1 \\ \\ y=(x-2)^2+1\]

Answer 8

A little confusing but I think I understand, thank you!