SOLUTION: Find an equation of the parabola which contains a minimum point at (2,-1) and ordered pair (-1,7)

Here are the points plotted:



The equation of a parabola with vertex (h,k) is

y = a(x - h)² + k

The vertex is the minimum point, so

(h,k) = (2,-1)

We substitute h and k

y = a(x - 2)² + (-1)

y = a(x - 2)² - 1

So we have everything but 'a'.

So we substitute the point (x,y) = (-1,7)

7 = a(-1 - 2)² - 1

 7 = a(-3)² - 1

 7 = a(9) - 1

 7 = 9a - 1

 8 = 9a

 = a

So the equation of the parabola is

y = (x - 2)² - 1


 
Edwin