Question

Rewrite the equation in vertex form. then find the vertex of the graph. y=-3x^2-5x+1

Answer 1

Answer: y = -3(x +
`(5)/(6)`)² +
`(37)/(12)`,
`(-(5)/(6)`,
`(37)/(12))`

Explanation:

First, you need to complete the square:

y = -3x² - 5x + 1

-1 -1

y - 1 = -3x² - 5x

y - 1 = -3(x² +
`(5)/(3)x`

y - 1 + -3(
`(25)/(36)`) = -3(x² +
`(5)/(3)x` +
`(25)/(36)`)

↑ ↓ ↑

`(5)/(3*2)` =
`((5)/(3*2))^(2)`

y - 1 -
`(25)/(12)` = -3(x +
`(5)/(6)`)²

y -
`(12)/(12)` -
`(25)/(12)` = -3(x +
`(5)/(6)`)²

y -
`(37)/(12)` = -3(x +
`(5)/(6)`)²

y = -3(x +
`(5)/(6)`)² +
`(37)/(12)`

Now, it is in the form of y = a(x - h)² + k where (h, k) is the vertex

Vertex =
`(-(5)/(6)`,
`(37)/(12))`