Write the quadratic equation in standard form that represents the table below:
20 POINTS IF YOU HELP!

x^2 - 3x + 2

Step-by-step explanation:

formula for quadratic equation

y = ax^2 + bx + c

to solve this, we need at least three points

use (1, 0), (0, 2), and (-1, 6)

since the y-intercept is at (0,2), c = 2

plug in values for (1,0), x= 1, y = 0, c = 2

y = ax^2 + bx + c

0 = a(1^2) + b(1) + 2

0 = a + b + 2

write a in terms of b

a = - b - 2

plug in values for (-1, 6), x = -1, y = 6, c = 2

6 = a(-1^2) + b(-1) + 2

6 = a - b + 2

4 = a - b

so we have two equations, plug a into the second equation

a = - b - 2

4 = a - b

4 = (-b - 2) - b = -2b - 2

b = -3

plug b back into a = - b - 1

a = -(-3) - 2 = 1

plug a, b, and c back into y = ax^2 + bx + c

so your equation is x^2 - 3x + 2

sorry but i cant draw that