Question 846713
To find the equation of the parabola in the standard form of ax^2 + bx + c, given the two zeroes, we need to place the zeroes in factor form.  When zeroes are fractions, take the denominator of each fraction and place it in front of the x in each factor, and use the numerator as our constant, and use the opposite sign of our zeroes.  For example, if one of our zeroes is 1/5, we would put this in factor form as (5x - 1), because we put the denominator (5) in front of x and use the numerator (1) as our constant, and the sign we would use is the opposite of the sign of the zero.  The zero is a positive fraction, so we will use a MINUS sign.  So, using these steps, we can put each of our given zeroes in factor form:


-5/3 = (3x + 5)


7/2 = (2x - 7)


Now that we have our two factors, all we need to do is multiply them using the FOIL method:


(3x + 5)(2x - 7) ----->


6x^2 - 21x + 10x - 35 ----->


6x^2 - 11x - 35


Therefore, the equation of a parabola in standard form y = ax^2 + bx + c, with the zeroes -5/3 and 7/2 (and with integers with no common factors, and with a > 0) is:


y = 6x^2 - 11x - 35