Write an equation for a parabola with vertex at (1,-3) with an x-intercept of 4.

Answer 1

y=a(x-h)^2+k

vertex =(1,-3)

substitute

y=a(x-1)^2-3

the x-intercept occurs when y=0

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

let x=4

substitute

0=a(4-1)^2-3

0=a(3)^2-3

0=a(9)-3

3=9a

a=3/9

a=1/3

y=(1/3)(x-1)^2-3, or...

3y=(x-1)^2-9