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Stitz-Zeager_College_Algebra_e-book

To that end we recall that a2 b2 c2 so b2 c2 a2 25

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Unformatted text preview: is squared, we can attempt to put the equation into a standard form using the following steps. To Write the Equation of a Parabola in Standard Form 1. Group the variable which is squared on one side of the equation and position the non-squared variable and the constant on the other side. 2. Complete the square if necessary and divide by the coefficient of the perfect square. 3. Factor out the coefficient of the non-squared variable from it and the constant. 412 Hooked on Conics Example 7.3.4. Consider the equation y 2 + 4y + 8x = 4. Put this equation into standard form and graph the parabola. Find the vertex, focus, and directrix. Solution. We need to get a perfect square (in this case, using y ) on the left-hand side of the equation and factor out the coefficient of the non-squared variable (in this case, the x) on the other. y 2 + 4y + 8x y 2 + 4y y 2 + 4y + 4 (y + 2)2 (y + 2)2 = = = = = 4 −8x + 4 −8x + 4 + 4 complete the square in y only −8x + 8 factor −8(x − 1) Now that the equation is in the form given in Equation 7.3, we see that x − h is x − 1 so h = 1, and y − k is y + 2 so k = −2. Hence, the vertex is (1,...
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