Suppose that we have an equation y=ax^2+bx+c whose graph is a parabola with vertex (3,2), vertical axis of symmetry, and contains the point (1,0). What is (a, b, c)?

Corbella.15 Oct 10, 2019

#1**+1 **

If the vertex is (3,2) and it contains the point (1,0).....then x = 1 is a root

So...by symmetry......(5, 0) is also a root

So....we can find "a" thusly

0 = a(1 - 3)^2 + 2

-2 = a(-2)^2

-2 = 4a

a = -2/4 = -1/2

And by Vieta......

The sum of the roots -b/a

So

1 + 5 = - b / ( -1/2)

6 = 2b

b = 3

And the product of the roots = c/a

So

5*1 = c /(-1/2)

5 = -2c

c = -5/2

So

(a,b , c) = ( -1/2, 3, -5/2)

Here's the graph : https://www.desmos.com/calculator/yd99xbrpsg

CPhill Oct 10, 2019