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Text Box: Math 1314
College Algebra

LO-12
Chapter Appendix II (Parabola)

Skills to Master

·       Recognize and use the standard equation for a parabola that opens up or down

·       Recognize and use the standard equation for a parabola that opens left or right


·        

The Parabola

You studied the parabola as a function in chapter 3.  Parabolas are another kind of conic section.  We are not concerned with examining the parabola as a function but, like the circle before, as a set of points related by a general form of an equation.  We will look at parabolas that open either up or down and also at parabolas opening to the left or to the right.

The standard form of a parabola opening up or down is , where h and k are the x- and y-coordinates of the vertex and the value of a will determine whether the parabola opens up or down.  As before, if  (positive), then the parabola opens up; if  (negative), then the parabola opens down.

The standard form of a parabola that opens left or right is the same as above but with the variables x and y exchanged and the values of h and k exchanged.  That is, .  For this form, if  (positive), the parabola opens to the right; if  (negative), the parabola opens to the left.

Example


 

 


 


 

Example

Find the equation of the parabola with the given properties.

With vertex at (0, 2), opening up and passing through (1, 4).

 

 

With vertex at (3, -4), opening to the left, and passing through (-1, -6).

 

 

With vertex at (2, 1), opening to the right, and passing through (4, 3).

 

 

With vertex at (-1, -3), opening down, and passing through (1, -15).