Points (-9,0) and (19,0) lie on the curve of a parabola.

Question

What is the axis of symmetry for the parabola?

Answer 1

The given points (-9,0) and (19,0)

The distance to the middle point x = (19+(-9))/2

x = 10/2 = 5

The equation is x = 5

Therefore x = -b/2a

5 = -b/2a

10a = -b

Therefore a = -1 and b =10

The symmetry parabola equation is y = ax^2+bx+c

Substitute x = -9, y = 0 in the above equation

0 = (-1) (-9)^2+10(-9) +c

0 = - 81-90+c

Therefore c = 171

Substitute the values of a = -1,b =10 and c = 171 in  parabola equation

The symmetry parabola equation is y = -x^2 +10x +171

The graph of the parabola is

Comments

The axis of symmetry is x = (- 9 + 19) / 2 = 10 / 2 = 5.