Based on the calculations, an equation which best models the graph is N(x) = -3x² + 22x + 52 = 0.
<h3>The standard form of a quadratic equation.</h3>
In Mathematics, the standard form of a quadratic equation is given by ax² + bx + c = 0.
Taking the data values for the graph as follows:
<u>Museum Visitors</u>
Day of Week, x: 1 2 3 4 5 6 7
Number of Visitors, N(x): 71 84 91 92 87 76 59
For each day of the week, we would write the quadratic equation as follows:
f(x = 1) = a(1)² + b(1) + c = 71 = a + b + c .....equation 1.
f(x = 2) = a(2)² + b(2) + c = 84 = 4a + 2b + c .....equation 2.
f(x = 3) = a(3)² + b(3) + c = 91 = 9a + 3b + c .....equation 3.
Solving the equations simultaneously, we have:
a = -3
b = 22
c = 52
Therefore, the quadratic equation is given by:
N(x) = ax² + bx + c = 0.
N(x) = -3x² + 22x + 52 = 0.
Read more on quadratic equation here: brainly.com/question/1214333
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