Plotting the magnitude response of a biquad filter I've put together a multi-band audio EQ using biquad filters.  I'm getting the coefficients using the methods from the RBJ cookbook.

Now I want to plot the curve showing the magnitude response.  I'm using an equation from this source

Here is my function to get the coefficients and get the magnitude response at points of interest.

void GetCoefficients (double samplerate = 44100.0) {

    //from the rbj biquad coefficient cookbook by Robert Bristow-Johnson
    long double SR = (long double)samplerate;
    long double A = powl(10.0L, dBGain/40.0L);
    long double W0 = 2.0L * PI * Center / SR;
    long double alpha = sinl(W0)*sinhl( LN2/2.0L * WidthInOctaves * W0/sinl(W0));

    if (Type == "peaking") {
        b0 = 1.0L + alpha * A;
        b1 = -2.0L * cosl(W0);
        b2 = 1.0L - alpha * A;
        a0 = 1.0L + alpha / A;
        a1 = -2.0L * cosl(W0);
        a2 = 1.0L - alpha / A;
    }

    long double w;
    long double numerator;
    long double denominator;
    long double magnitude;

    for (int i = 0; i &lt; 59; ++ i) {
        w = 2.0L*PI*FreqPoints[i] / SR;  
        numerator = b0*b0 + b1*b1 + b2*b2 + 2.0L*(b0*b1 + b1*b2)*cosl(w) + 2.0L*b0*b2*cosl(2.0L*w);
        denominator = 1.0L + a1*a1 + a2*a2 + 2.0L*(a1 + a1*a2)*cosl(w) + 2.0L*a2*cosl(2.0L*w);
        magnitude = sqrtl(numerator / denominator);
        FrequencyResponse[i] = magnitude;   
    }
}


My filters sound correct, but my plot seams way wrong.  For example, when I have calculated the coefficients for a peaking filter with a width of $2$ octaves, centered at $4398\textrm{ Hz}$, with $3\textrm{ dB}$ gain; my magnitude response using those coefficients at $349\textrm{ Hz}$ is about $12$.  

I must be doing something wrong, but I can't quite figure it out.
Someone over at the KRV forum pointed out that I need to normalize my coefficients so that a0 = 1.

b0 /= a0;
b1 /= a0;
b2 /= a0;
a1 /= a0;
a2 /= a0;
a0 = 1;


Solved my problem.