Question

The line x=3 is the axis of symmetry for the graph of a parabola contains points (1,0) and (4, -3), what is the equation for the parabola?

Answer 1

Equation of the parabola: y = ax^2 + bx + c. Find a, b, and c.

x of axis of symmetry: `x = -b/(2a) = 3` -> b = -6a
Writing that the graph passing at point (1, 0) and point (4, -3):
(1) 0 = a + b + c -> c = - a - b = - a + 6a = 5a

(2) -3 = 16a + 4b + c --> -3 = 16a - 24a + 5a = -3a --> a = 1

b = -6a = -6; and c = 5a = 5

`y = x^2 - 6x + 5`

Check with x = 1: -> y = 1 - 6 + 5 = 0. OK