1. Find the equations of all tangents to the graph f(x) = x^2-4x + 25 that pass through the origin. 2. The relevant equations to my knowledge are the slope formula and f ' (x) 3. First I found the derivative using various rules to be f ' (x) = 2x - 4 after this i used the slope formula and my given point (0,0) to fill in this equation for slope m = 0 - X^2 +4x - 25 0-x I then simplified to this by canceling the negatives of the numerator and denominator and by then moving the denominator to the top by making the exponent a negative and then multiplied the trinomial by the monomial to get m = x +4 - (25/x) after this I set m = f ' (x) in order to find the values of x where the tangent line will pass through (0,0). I got -x-(25/x) = 0 however this function does not have any zeros and therefore can not be the equation I'm looking for because the slopes i should get according to the answer key are m = -14 and m = 6 Any help would be greatly appreciated.