Question

Hi. I need help with these questions. See image for question. Please answer no 10 and 11

Answer 1

9514 1404 393

Answer:

  10. (x, y) = (-3/8, 2 9/16)

  11. k = -1

Step-by-step 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.