Modeling this scenario with a system of equations using a linear function and a quadratic function yields the following:
y = 2(x - 4)² + 2.
5x + 11y = 62.
<h3>What is the quadratic equation?</h3>
A quadratic function with vertex (h,k), may be represented by the equation:
y = a(x - h)² + k
Because the vertex of this issue is located at (4,2), we may deduce that h = 4 and k = 2, and the equation for this problem is as follows:
y = a(x - 4)² + 2.
Because it goes through the location characterized by its coordinates (5, 4), we may determine a by establishing that when x = 5, y = 4.
4 = a + 2.
a = 2.
Thus the equation is:
y = 2(x - 4)² + 2.
The slope, denoted by m, is the rate of change, or the degree to which y deviates from its initial value for each unit of x that is added.
The y-intercept, denoted by the letter b, is the value of the variable y when the variable x is equal to zero. It may also be construed as the beginning value of the function.
Because the road links the locations (–3, 7) and (8, 2), the slope may be calculated as follows:
m = (2 - 7)/(8 - (-3)) = -5/11.
Then:
y = -5/11x + b.
When x = 8, y = 2, hence we use it to find b as follows:
2 = -40/11 + b
b = 62/11.
Then the equation is:
y = -5/11x + 62/11.
5x + 11y = 62.
The system of equations is:
y = 2(x - 4)² + 2.
5x + 11y = 62.
More can be learned about a system of equations at brainly.com/question/24342899
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