clear
format compact

e1 = exp(1);
c0 = (e1 - 1/e1)*(1/2);
c1 = (2/e1)*(1+1/2);
c2 = ((e1 - 7/e1))*(2+1/2);

p0 = @(x) 1;
p1 = @(x) x;
p2 = @(x) (3*x.^2 - 1)/2;

appr1 = @(x) c0*p0(x) + c1*p1(x);
appr2 = @(x) c0*p0(x) + c1*p1(x) + c2*p2(x);

x = linspace(-1, 1, 100);

plot(x, exp(x), '-')
hold on
plot(x, appr1(x), '--')
plot(x, appr2(x), '--')
grid on
legend('exp(x)', 'linear approx.', 'quadratic approx.', 'location', 'best')
xlabel('x')