Question

Find the minimum value of the parabola y = x2 – 2x – 3.

Answer 1

- 4

Explanation:

the minimum value of the parabola is the value of the y- coordinate of the vertex.

given a parabola in standard form

y = ax² + bx + c ( a ≠ 0 )

then the x- coordinate of the vertex is

x = -
`(b)/(2a)`

y = x² - 2x - 3 ← is in standard form

with a = 1 and b = - 2 , then

`x_(vertex)` = -
`(-2)/(2)` = 1

substitute x = 1 into the equation for corresponding y- coordinate

y = 1² - 2(1) - 3 = 1 - 2 - 3 = - 4

then minimum value is - 4