Question

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

Answer 1

f(x)= -x²-4x-2

Step-by-step explanation (this way is not the shortest one):

1. for intercept (-2-√2;0): a(-2-√2)²+b(-2-√2)+c=0

for intercept (-2+√2;0): a(-2+√2)²+b(-2+√2)+c=0

for the point (-1;1): a(-1)²+b(-1)+c=1

2. using the three record written above, it is possible to make up the system of equations and calculate 'a', 'b' and 'c':

3. the required equation is: -x²-4x-2