Find the equation

Question

Find the equation of the parabola satisfying: focus at (6,1) vertex at (6,6). Express this equation in general form.

Answer 1

Hi Mateo,

 

Let's begin by writing the equation of a parabola in vertex form and plug in the coordinates of our vertex:

    y = a(x - h)² + k  [vertex form, vertex = (h,k)]

    y = a(x - 6)² + 6

 

Now let's calculate coefficient (a) using the distance (c) from the vertex to the focus.  Note that the sign of coefficient (a) will be negative, since the vertex is above the focus:

    c = 1 - 6 = -5

    a = 1/4c

    a = 1/[(4)(-5)]

    a = -(1/20)

    a = -0.05

 

Finally, we'll transform our equation from vertex form to general form (y = ax² + bx + c):

    y = a(x - h)² + k  [vertex form, vertex = (h,k)]

    y = -0.05(x - 6)² + 6 

    y = -0.05(x² - 12x + 36) + 6

    y = -0.05x² + 0.6x - 1.8 +6

    y = -0.05x² + 0.6x + 4.2

 

Thanks for submitting this problem and glad to help.

 

God bless, Jordan.

Answer 2

The solution provided is great except for at almost the last step. The negative must be distributed as follows:

 

y = -0.05(x² - 12x + 36) + 6
y = -0.05x_² + 0.6x - 1.8 +6
y = -0.05x² + 0.6x + 4.2