Question

Write the equation of a parabola, in standard form, that goes through these points: (0, 3) (1, 4) (-1, -6)

Answer 1

Hello,

P:y=ax²+bx+c is the equation.

(0,3)∈P==>3=a*0+b*0+c==>c=3
(1,4)∈P==>4=a+b+3==>a+b=1 (1)
(-1,-6)∈P==>-6=a-b+3==>a-b=-3 (2)

(1)+(2)==>2a=-2==>a=-1
(1)==>b=1-(-1)==>b=2

y=x²+2x+3
y=(x+1)²+2
Vertex is (-1,2)