BACCALAURÉAT GÉNÉRAL ET TECHNOLOGIQUE SESSION 2009 ÉPREUVE SPÉCIFIQUE MENTION « SECTION EUROPÉENNE OU DE LANGUE ORIENTALE »
Académies de Paris-Créteil-Versailles Binôme : Anglais / Mathématiques Sujet 9 PARABOLAS The first part of this page is a summary that can help you to do the exercise. ► Let a, b, c be three real numbers, with a ≠ 0. Let P be the graph whose equation is y = ax2 + bx + c. P is called a parabola, a line-symmetric curve. b The x-coordinate of the vertex is − 2a ► Solving the quadratic equation: ax 2 + bx + c = 0 with a ≠ 0. b 2 − 4ac is called the discriminant. When the discriminant is positive, the solutions of the quadratic equation are given by the quadratic formula x =
−b ± b 2 − 4ac . 2a
When the discriminant is zero, there is one real number solution x =
−b called a double root of the 2a
equation. When the discriminant is negative, there is no real number solution.
Exercise: Suppose that a chimpanzee is in a tree 14 metres above the ground and it decides to use a vine to swing to another tree. One second after beginning his swing, it is 10.5 metres above the ground. Five seconds after beginning his swing, it is 6.5 metres above the ground. We want to write the height of the chimpanzee h, as a quadratic function of t, t being the number of seconds after beginning his swing. a. Using the text, state three values for (t, h). b. Write an equation for the parabola that passes through these points. c. Sketch the graph of the parabola. d. How closer is the chimpanzee from the ground when swinging?
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