Since we can not determine the exact value with just seeing the graph, it would be necessary to find the equation of the parabola and find the vertex.
y = a*x^2 + b*x + c
We can use the point (0, 10) to find c
10= a*(0)^2 + b*(0) + c (Replacing x=0 (t=0) and y=10)
10 = c
Replacing the points (1.5 , 75) and (3.5, 90), we have
75= a*(1.5)^2 + b*(1.5) + 10 (Equation 1)
75= 2.25*a + 1.5*b + 10 (Raising 1.5 to the power of 2) (Equation 1)
65 = 2.25*a + 1.5*b (Subtracting 10 from both sides of the equation)(Equation 1)
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90= a*(3.5)^2 + b*(3.5) + 10 (Equation 2)
90= 12.25*a + 3.5*b + 10 (Raising 3.5 to the power of 2) (Equation 2)
80= 12.25*a + 3.5*b (Subtracting 10 from both sides of the equation)(Equation 2)
We are going to solve the system with the elimination method.
-455 = -15.75*a - 10.5*b (Multiplying equation 1 by -7)
+ 240= 36.75*a + 10.5*b (Multiplying equation 1 by 3)
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-215 = 21*a (Adding equations)
-215/21 = a (Dividing by 21 on both sides of the equation)
-10.238=a (Dividing)
Replacing a=-10.328 in the equation 1, we have:
-455 = -15.75*(-10.328) - 10.5*b
-455 = +162.666 - 10.5*b (Multiplying)
-455 - 162.666 = - 10.5*b (Subtracting 162.666 from both sides of the equation)
-617.334 = -10.5*b
b = 58.825 (Dividing by -10.5 on both sides of the equation)
Using the formula for the vertex of the parabola we have:
Vx= -b/ (2a)
Vx= -58.825/(2*10.5)
Vx= 2.8
Replacing Vx in the parabola we have:
y = (-10.238)*(2.8)^2 + (58.825)*(2.8) + 10
y= 94.44
The answer is 94 rounded to the nearest meter.