How do you write the equation for a graph that is a parabola with a vertex at (5, 3)(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+ky=a(xh)2+k
You have h = 5h=5 and k=3k=3 but no (x,y)(x,y) so then the equation becomes just y=a(x-5)^2 + 3y=a(x5)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) + 3y=a(x210x+25)+3

Explanation:

y = ax^2 + bx + cy=ax2+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