Question

Which equation is y = 3(x – 2)2 – (x – 5)2 rewritten in vertex form? Y = 3 (x minus seven-halves) squared minus StartFraction 27 Over 4 EndFraction y = 2 (x minus 1) squared minus 11 y = 2 (x minus one-half) squared minus StartFraction 53 Over 4 EndFraction y = 2 (x minus one-half) squared minus StartFraction 27 Over 2 EndFraction

Answer 1

i got y=2(x-1/2)^2- 27/2 so the last one is right

Explanation:

:)

Answer 2

Answer: y = 2 (x minus one-half) squared minus StartFraction 27 Over 2 EndFraction

or

`y=2((x-(1)/(2))^2)-(27)/(2)`

Explanation:

Vertex form of equation :
`f (x) = a(x - h)^2 + k,`where (h, k) is the vertex of the parabola.

`y=3(x-2)^2-(x-5)^2\\\\=3(x^2+4-4x)-(x^2+25-10x)\\\\=3x^2+12-12x-x^2-25+10x\\\\=2x^2-2x-13\\\\=2(x^2-x-(13)/(2))\\\\=2(x^2-x+(1)/(4)-(1)/(4)-(13)/(2))\\\\=2((x-(1)/(2))^2-(1+26)/(4))\\\\=2((x-(1)/(2))^2-(27)/(4))=2((x-(1)/(2))^2)-(27)/(2)`

Hence, the vertex form of the equation is
`y=2((x-(1)/(2))^2)-(27)/(2)`