Write the equation for the parabola that has x− intercepts (−2 − square root of 2 ,0) and (−2 + square root of 2 ,0) and passes through the point(−1,1).

Question

Please tell me what the equation is please!!!

Answer 1

the equation is obviously y = ax² + bx + c and all three of these points satisfy it:

(-2-√2,0)  (-2+√2,0)   (-1,1).

 

Substitute these values in, getting three equations with unknowns a, b, c.  Solve ! 

Answer 2

y=a(x-p)(x-q)

y=a(x+2+√2)(x+2-√2)

passing through point (-1,1)

substitute

1=a(-1+2+√2)(-1+2-√2)

1=a(1+√2)(1-√2)

1=a(1-2)

1=a(-1)

a=1/(-1)

a=-1

y=-(x+[2+√2])(x+[2-√2])

y=-(x²+4x+2)