Match the equation on the left with the graph on the right.
  1. y − 2 = (x + 1)2 ________
  2. y − 1 = -½(x + 2)2 ________
  3. y − x2 = 2 ________
  4. y = x2 + 4x + 5 ________
  5. y = x2 − 4x + 5 ________
Write an equation of the parabola satisfying the given conditions.
  1. The vertex is (3, -2); the parabola contains (2, 0) and (4, 0). ________________________
  2. The axis is x = 2; the parabola contains the origin and (1, 6). ________________________
  3. The x-intercepts are 3 and 7; the minimum value of y is -6. ________________________
In exercises 9-15, refer to the function f(x) = -3 − 4x − ½x2.
  1. Find the vertex of the graph of f. ___________
  2. Find the domain of f. ______________
  3. Find the range of f. ________________
  4. Find the zeros of f. _______________
  5. Does f have a maximum or does it have a minimum? ______________
  6. What is the maximum or minimum value of f? _________________
  7. What is the value of x for which the value of f is a maximum or minimum? ______________
Write a quadratic equation with integral coefficients having the given roots.
16.  -3 (a double root) ____________17.  5, -3 ____________
18.   2 + √5, 2 − √5 ____________19.  4, ¾ ____________
20.  3i, -3i ____________21.  5 + 3i, 5 − 3i ____________

22.  The sum of the lengths of the legs of a right triangle is 10 cm. What is the greatest area of such a triangle?
Answers:
1.  c
2.  d
3.  b
4.  e
5.  a
6.  y = 2(x − 3)2 − 2
7.  y = -2(x − 2)2 + 8
8.  y = (x − 5)2 - 6
9.  (-4, 5)
10. all reals
  1. (-∞, 5]
  2. {-4 ± √(10)}
  3. maximum
  4. max is 5
  5. max at x = -4
  6. y = a(x + 3)2 or
    y = a(x2 + 6x + 9)
  7. y = a(x − 5)(x + 3)
    or y = a(x2 − 2x − 15)
  1. y = a[x − (2 + √5)][x − (2 − √5)]
    or y = a(x2 − 4x − 1)
  2. y = a(x − 4)(x − ¾),
    take a=4: 4(x − 4)(x − ¾)=4x2 − 19x + 12
  3. y = a(x − 3i)(x + 3i) or y = a(x2 + 9)
  4. y = a[x − (5 + 3i)][x − (5 − 3i)]
    or y=a(x2 − 10x + 34)
  5. 12.5 cm2