how to find the y axis and xaxis of a paradola

Question

i would appreciate help thanks

Answer 1

Once you understand this you will become a master...Keys to remember: imagine a coordinate plane...

    a simple example to consider...for every value 'x' there is an equal, but opposite value for 'y' so that the difference of the product of the x² and y² = 0       equation will be x²  -  y²

    the first one is easy...when 'x = 0', then 'y = 0'  that's the place to begin...vertex is the origin

              now imagine a table  like              x      0      ?      ?      ?      ?   

                                                              y      0      ?      ?      ?      ?

              with   ( 0,0 )  being the vertex, when  x = 1, then y = 1          x      0       1       ?       ?       ?                                                                                                            y      0      1       ?       ?       ?

           this satisfies the equation x²  -  y²     but  x = -1   y = 1            x       0       1      -1       ?       ?   

                                                                                                      y       0       1        1       ?       ?

     this satisfies the equation x²  -  y²    but x = 2 y = 2                       x       0       1      -1       2       ? 

                                                                                                      y       0       1       1       2       ?

   this satisfies the equation x²  -  y²   , too  what if x = 5 y = 5             x       0       1      -1       2       5

                                                                                                      y       0       1       1       2       5

  this also satisfies the equation x²  -   y²   but consider    x = -11  y = 11    or    x = -11   y = 11    also remember, the vertex doesn't always have to be ( 0, 0 ):    make some extrapolations...what if all x's were positive, what could the y-values be? What if all the x-values were all negative, what might be the possible y-values? Something to think about...what if all the y-values were  negative?

the first rule...where x² - y² but the difference doesn't always have to be zero. parabolas can be open: right side up...upside down...open to the right...and open to the left. Starting at the origin is an easy to get the concept...but more complicated problems exist...when x²  -  y²  ≠  0.  Do you think that would be a parabola?

Answer 2

The axis of symmetry is always at x=-b/2a for a vertical parabola, while the y-intercept is the constant "c".  Algebra 1 mostly deals with vertical parabolas, while algebra 2 introduces horizontal parabolas during the conic sections chapter.  y=ax^2+bx+c is standard form of Vertical, while x=ay^2+by+c is for Horizontal parabolas. In addition, Alg 2 will introduce the directrix and focus point on a parabola.  Good luck and I hope this helps.