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Unformatted text preview: MAP 103: Proﬁciency Algebra Homework #10
DUE: THURSDAY, NOV. 12, 2009 1. Apply completing the square to ﬁnd the roots to the quadratic equation 2x2 − px − 1 = 0. Here p is an arbitrary real number. 2. Apply completing the square to ﬁnd the roots to the quadratic equation 3x2 + 9x − 12 = 0. 3. Let f (x) = (x + 1)2 + 2. Find f (0) and determine the range of f (x). Write the range in interval notation. 4. A quadratic polynomial has the roots x = −2 and x = 3. Find the equation for the polynomial in the form ax2 + bx + c = 0. 5. The quadratic function f (x) = x2 + 6x + 9 has the repeated root x = −3. Show that the vertex, v, has coordinates v = (−3, 0). 6. Consider the quadratic function f (x) = x2 + 2x + 4. Find the equation for the axis of symmetry and ﬁnd the coordinates for the zeros (roots). 7. Given p(x) = −(x − 2)2 + 3. Will the graph of p(x) show that p(x) is a maximum value curve or a minimum value curve? Hint: Look at the vertex of p(x). 8. A triangle has area 12. If the base has length x + 1 and the height has length x + 6, ﬁnd the measurements of the triangle. Check your solution. 9. Let g (x) = 2x2 − x − 3. What is the nature of the roots of g (x)? 10. Use the discriminant, D = b2 − 4ac, to ﬁnd the nature of the roots for a quadratic function of the form p(x) = −kx2 − 2k + 1. k is an arbitrary real number. Hint: Here a = −k, b = −2k, c = 1. ...
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This note was uploaded on 04/18/2010 for the course MAP 103 taught by Professor Staff during the Fall '08 term at SUNY Stony Brook.
- Fall '08