vertex (6, −5); point (7, 2) Write out thre function

Question

Find a function f whose graph is a parabola with the given vertex and that passes through the given point.

Answer 1

V(6,-5)   P(7,2)     So, by plotting those two points, you can tell the parabola opens up.

y - k = a(x-h)²     V(h,k)      Replace x and y with 7 and 2.

2 - 5 = a(7 - 6)² 

-3 = a

y-5 = -3(x-6)²

 

 

 

Answer 2

f(x) = A(x-6)² - 5

 

Since (7,2) lies on the graph, we have 2 = A(7-6)² - 5

 

So, A = 7

 

Therefore, f(x) = 7(x-6)² - 5