SOLUTION: Identify the conic section represented by each equation. If it is a parabola, give the vertex. If it is a circle, give the center and radius. If it is an ellipse or a hyberbola, gi

Question 79487This question is from textbook Algebra 2
: Identify the conic section represented by each equation. If it is a parabola, give the vertex. If it is a circle, give the center and radius. If it is an ellipse or a hyberbola, give the center and foci. Sketch the graph.
This question is from textbook Algebra 2

Answer by Edwin McCravy(20060) (Show Source): You can put this solution on YOUR website!
Identify the conic section represented by each equation. If it is a parabola, give the vertex. If it is a circle, give the center and radius. If it is an ellipse or a hyberbola, give the center and foci. Sketch the graph.

It is a parabola because it only has ONE squared letter.
Get all the terms in the squared letter on the left and
all other terms on the right:

Factor out the coefficient of on the left:

Complete the square by adding 1 inside the parentheses
on the left. However note that when we placing a 1
inside the parentheses on the left, we are really adding 3
because of the 3 multiplier in front of the parentheses
so we must add 3 to the right side to offset.

Factor the trinomial on the left side as a perfect square,
and combine terms on the right:

Multiply both sides by

Now the equation is in the form:

where the vertex is (h,k) = (2,1)

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