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Answer:
10. (x, y) = (-3/8, 2 9/16)
11. k = -1
Explanation:
10. The value of x at the vertex is ...
x = -b/(2a)
x = -(-3)/(2(-4)) = -3/8
The corresponding value of y is ...
y = 2 +(-3/8)(-3 +(-3/8)(-4)) = 2 +(-3/8)(-3/2) = 2 +(9/16)
The vertex is (x, y) = (-3/8, 2 9/16).
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11. The discriminant is zero when the roots are equal.
b² -4ac = 0
(k-1)² -4(1)(-k) = 0
k² -2k +1 +4k = 0
k² +2k +1 = 0 . . . . . collect terms
(k +1)² = 0 . . . . . . . . write as a square
k = -1 . . . . . . . . . . . . the value of k that satisfies
Check
x² -2x +1 = (x -1)² = 0 . . . . has equal roots: x=1.