How do you write the equation for a graph that is a parabola with a vertex at #(5, 3)#?

2 Answers
Jul 24, 2017

You can't find any graph with just one point. If you just have a point it's just a point.

Explanation:

You can't find the equation for a parabola with just a vertex. You need another point.

The equation for a parabola is #y=a(x-h)^2+k#
You have #h = 5# and #k=3# but no #(x,y)# so then the equation becomes just #y=a(x-5)^2 + 3# which is not enough information to get the equation.

You can't find any graph with just one point. If you just have a point it's just a point.

Jul 24, 2017

#y = a(x^2 - 10x + 25) + 3#

Explanation:

#y = ax^2 + bx + c#

#-b/(2a) = 5 and - Delta/(4a) = 3#

#b = -10a and Delta = -12a = 100a^2 - 4ac => c = 25a + 3#

#y = ax^2 - 10ax + 25a + 3#

Example:

#x^2 - 10x + 28 = 0#
#Delta = 100 - 4 * 28 = -12#
#x = 5 ± i sqrt 3#