Question

If x is real, then the minimum value of x²−8x+17 is __
A. 1
B. 2
C. 3
D. 4

Answer 1

A

Explanation:

the minimum value of the quadratic expression is the value of the y- coordinate of the vertex.

given a quadratic expression in standard form

ax² + bx + c ( a ≠ 0 ) , then

the x- coordinate of the vertex is

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

x² - 8x + 17 ← is in standard form

with a = 1 and b = - 8 , then

`x_(vertex)` = -
`(-8)/(2)` = - (- 4) = 4

substitute x = 4 into the expression and evaluate

4² - 8(4) + 17 = 16 - 32 + 17 = - 16 + 17 = 1

the minimum value is then 1