Answer:
roots are 11 and -1. vertex is (5, -36).
Explanation:
The calculator will give answer when in a quadratic equation mode (calculators vary).
but we can also solve this by completing the square.
X ² - 10x - 11 = 0
1) put the x, not x ², in parenthesis.
2) half the coefficient (10) of x. that is 5. Put that into same parenthesis.
3) we have (x - 5)
4) Subtract (-5) ² = 25 from this.
5) [(x - 5) ² - 25] – 11 = 0
6) now we have (X - 5) ² – 36 =0
7) (x - 5) ² = 36
8) (x - 5) = ± √36
9) x = ±6 + 5. so x = 11 or x = -1. these are the roots.
the vertex is given by (X - 5) ² – 36. the x-coordinate is the number inside the bracket (but reversed), the y-coordinate is the number outside the bracket. so the vertex is at (+5 , -36) = (5, -36)