Question

Please help! I've tried this problem many times but continue to get it wrong.

write the function in vertex form y= -x^2-3x-1

Answer 1

y =- (x +
`(3)/(2)`)² +
`(5)/(4)`

Explanation:

the equation of a parabola in vertex form is

y = a(x - h)² + k

where (h, k) are the coordinates of the vertex and a is a multiplier

To obtain this form use the method of completing the square

• the coefficient of the x² term must be 1

Take out a factor of - 1 from - x² - 3x

y = -(x² + 3x) - 1

• add/subtract (half the coefficient of the x-term)² to x² + 3x

y = - (x² + 2(
`(3)/(2)`)x +
`(9)/(4)` -
`(9)/(4)`) - 1

y = -(x +
`(3)/(2)`)² +
`(9)/(4)` -
`(4)/(4)`

y = - (x +
`(3)/(2)`)² +
`(5)/(4)` ← in vertex form