set.seed(666)
x1 = rnorm(1000,0,1)           # some continuous variables
x2 = rnorm(1000,0,1)
z = 1 + 2*x1 + 3*x2        # linear combination with a bias

pr = 1/(1+exp(-z))         # pass through an inv-logit function
y = rbinom(length(x1),1,pr)      # bernoulli response variable

df = data.frame(y=y,x1=x1,x2=x2)
glm( y~x1+x2,data=df,family="binomial")

set.seed(666)
x1 = rnorm(1000,0,1)
z = 1 + 2*x1 + 3*x1^2
pr = 1/(1+exp(-z))
y = rbinom(length(x1),1,pr)
df = data.frame(y=y,
                x1=x1,
                x2=x1^2)
glm( y~x1+x2,
     data=df,
     family="binomial")

Call:  glm(formula = y ~ x1 + x2, family = "binomial", data = df)

Coefficients:
(Intercept)           x1           x2
      1.002        2.437        3.490

Degrees of Freedom: 999 Total (i.e. Null);  997 Residual
Null Deviance:      795.3
Residual Deviance: 615.9    AIC: 621.9
Warning message:
glm.fit: fitted probabilities numerically 0 or 1 occurred

set.seed(666)
x1 = rnorm(1000,10,1)
z = 1 + 2*x1 + 3*x1^2
pr = 1/(1+exp(-z))
y = rbinom(length(x1),1,pr)

df = data.frame(y=y,
                x1=x1,
                x2=x1^2)
glm( y~x1+x2,
     data=df,
     family="binomial")
Call:  glm(formula = y ~ x1 + x2, family = "binomial", data = df)

Coefficients:
  (Intercept)           x1           x2
2.657e+01   -2.351e-08    1.234e-09

Degrees of Freedom: 999 Total (i.e. Null);  997 Residual
Null Deviance:      0
Residual Deviance: 5.802e-09    AIC: 6
Warning message:
glm.fit: algorithm did not converge

set.seed(666)
x1 = rnorm(1000,10,1)
x1=scale(x1)
z = 1 + 2*x1 + 3*(x1)^2
pr = 1/(1+exp(-z))
y = rbinom(length(x1),1,pr)

df = data.frame(y=y,
                x1=x1,
                x2=x1^2)
glm( y~x1+x2,
     data=df,
     family="binomial")
Call:  glm(formula = y ~ x1 + x2, family = "binomial", data = df)

Coefficients:
(Intercept)           x1           x2
     0.9872       2.4292       3.5237

Degrees of Freedom: 999 Total (i.e. Null);  997 Residual
Null Deviance:      787.8
Residual Deviance: 605.7    AIC: 611.7
Warning message:
glm.fit: fitted probabilities numerically 0 or 1 occurred