Question

Which is the vertex of x2 + 10x = -17

(-5,-8)

(5,8)

(-5,8)

(5,-8)

Answer 1

vertex = (- 5, - 8)

Explanation:

Given a quadratic in standard form : ax² + bx + c = 0 : a ≠ 0

Then the x- coordinate of the vertex is

`x_(vertex)` = -
`(b)/(2a)`

Given x² + 10x = - 17 ( add 17 to both sides )

x² + 10x + 17 = 0 ← in standard form

with a = 1, b = 10, c = 17, then

`x_(vertex)` = -
`(10)/(2)` = - 5

Substitute x = - 5 into the quadratic for the corresponding value of y

y = (- 5)² + 10(- 5) + 17 = 25 - 50 + 17 = - 8

Hence vertex = (- 5, - 8)