quadratic equation of the parabola that goes through the points (-1,0)(4,0)(-0,-1)

Answer 1

two zeros are -1 and 4

f(x) = a(x+1)(x-4) = a(x^2 -3x -4) plug in the other point to solve for "a"

-1 = -4a

a = 1/4

f(x) = (1/4)(x^2 -3x -4)

4y = x^2 -3x -4 is an equation of a parabola through the given 3 points

the point (-0, -1) is a little strange, as 0 usually doesn't have a sign, + or -, suggesting a typo. Hopefully the only typo

but regardless, there could an infinite number of parabolas through the 3 points. but the most standard parabola is the upward opening one, with a vertical axis of symmetry. Other parabolas through the 3 points would be at angles, not up & down or left & right.