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A parabola has equation y = 4x^2 + x + c.
One x-intercept is -3. What is the value of c ?
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The condition says that if x= -3, then y = 0.
Let's write it as an equation
0 = 4*(-3)^2 + (-3) + c
or, simplifying
0 = 4*9 - 3 + c
0 = 36 - 3 + c
0 = 33 + c
c = -33.
ANSWER. c = -33.
CHECK. So, we found out the the function is y = 4x^2 + x - 33.
Let's substitute x= -3 in it. You will get
y = 4*(-3)^2 + (-3) - 33 = 4*9 - 3 - 33 = 36 - 3 - 33 = 0. ! Correct !
The problem is just solved.
Please write me if you do understand this solution in full.
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