Question

(0, -7) (2, 1) (5,-2)

Find a quadratic equation from three points, Alg 2

Answer 1

Explanation:

A quadratic equation is in the form of

`ax {}^(2) + bx + c`

C is the y intercept a.k.a the value of c is when x=0,

when x is 0, c is -7 so

c=-7

`{ax}^(2) + bx - 7`

Next we know when x is 2, y is 1 so

`a(2) {}^(2) + 2b - 7 = 1`

`4a + 2b = 8`

When x is 5, y is -2

`a(5) {}^(2) + b(5) - 7 = - 2`

`25a + 5b = 5`

So we have a system of equations, using elimination.

`5a + b = 1`

`- 6a = 6`

`a = - 1`

So

`5( - 1) + b = 1`

`b = 6`

Our quadratic is

`- {x}^(2) + 6x - 7`