Question 846713: Write the equation of a parabola in the form y=ax2 + bx + c where a,b, and c are integers with no common factors, a>0, and the zeros of the parabola are -5/3 and 7/2.
Answer by josh_jordan(263)   (Show Source):
You can put this solution on YOUR website! 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
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