Plot function in two intervals

I'm trying to plot an interval funciton like,

This is the code that I used

x = -3:0.001:3;
a = 1.3;
y = zeros(size(x));
for i = 1: length(x)
    if (x(i) >= -a && x(i)<=a)
        y(i) = 0.5*x(i).^2;
        
    else
        y(i) = a*abs(x(i))-a^2;
    end
end
plot (x,y)

But it did not plot this result.

Answer 1

[Image Analyst]

Try this (following your non-vectorized approach):

x = -4 : 0.001 : 4;
a = 1.3;
y = zeros(size(x));
for k = 1: length(x)
    if abs(x(k)) < a
        y(k) = 0.5*x(k).^2;
        
    else
        y(k) = a*abs(x(k))- 0.5 * a^2;
    end
end
plot (x, y, 'r-', 'LineWidth', 2)
grid on;

If you want a vectorized approach:

x = -4 : 0.001 : 4;
a = 1.3;
y = a*abs(x)- 0.5 * a^2;
innerX = abs(x) < a;
y(innerX) = 0.5*x(innerX).^2;
plot (x, y, 'r-', 'LineWidth', 2)
grid on;