Stitz-Zeager_College_Algebra_e-book

# Since the speed of sound is 760 miles per hour we can

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Unformatted text preview: e recognize this as the form given in Equation 7.3. Here, x − h is x + 1 so h = −1, and y − k is y − 2 so k = 2. Hence, the vertex is (−1, 2). We also see that 4p = 12 so p = 3. Since p > 0, the focus will be the right of the vertex and the parabola will open to the right. The distance from the vertex to the focus is |p| = 3, which means the focus is 3 units to the right. If we start at (−1, 2) and move right 3 units, we arrive at the focus (2, 2). The directrix, then, is 3 units to the left of the vertex and if we move left 3 units from (−1, 2), we’d be on the vertical line x = −4. Since the focal diameter is |4p| = 12, the parabola is 12 units wide at the focus, and thus there are points 6 units above and below the focus on the parabola. y 8 7 6 5 4 3 2 1 −5 −4 −3 −2 −1 −1 1 2 3 x −2 −3 −4 As with circles, not all parabolas will come to us in the forms in Equations 7.2 or 7.3. If we encounter an equation with two variables in which exactly one variable...
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