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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
y 2 + 4y + 8x
y 2 + 4y
y 2 + 4y + 4
(y + 2)2
(y + 2)2 =
−8x + 4
−8x + 4 + 4 complete the square in y only
−8x + 8
−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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