Find the quadratic equation that models the parabola containing the points: (-3,-56), (0,-2), (2,-16)

Answer 1

(-3, -56), (0,-2), (2,-16) are points on a parabola that appears to be downward opening, or it could be a leftward opening parabola, or an infinite number of other parabolas that are not vertical or horizontal

y= a(x-h) + k

-56 = a(-3-h)^2 + k

-2 = ah^2+ k

-16 = a(2-h)^2 + k

3 equations, 3 unknowns

-16 = ah^2 -4a + k

-2 = ah^2 + k

subtract

-14 = -4a

a = 14/4 = 7/2

a =3.5

-56 = a(h^2+6h + 9) +k

-56 = 3.5h^2 +21h + 31.5 + k

-2 = 3.5h^2 + k

subtract

-54 = 21h+ 31.5

21h = -54-31.5

h = -75.5/21

h = about 3.6

-2 = 3.5(3.6)^2 + k

k = -2 - 45.24

k =- 47.24

y = 3.5(x-3.6)^2 -47.24 is the equation through the three given points, an upward opening parabola

but there's also a leftward opening parabola and infinitely other slanted parabolas.