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 nonsquared
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 nonsquared 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 lefthand side of the
equation and factor out the coeﬃcient of the nonsquared 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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 Fall '13
 Wong
 Algebra, Trigonometry, Cartesian Coordinate System, The Land, The Waves, René Descartes, Euclidean geometry

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