Respuesta :
Using a linear function and a quadratic function, the system of equations that can be used to model this situation is:
- y = 2(x - 4)² + 2.
- 5x + 11y = 62.
What is the quadratic equation?
The equation of a quadratic function, of vertex (h,k), is given by:
y = a(x - h)² + k
In which a is the leading coefficient.
For this problem, the vertex is at (4,2), hence h = 4, k = 2 and the equation is:
y = a(x - 4)² + 2.
It passes through the point (5, 4), hence when x = 5, y = 4, which we use to find a.
4 = a + 2.
a = 2.
Thus the equation is:
y = 2(x - 4)² + 2.
What is the linear equation?
The linear equation is given by:
y = mx + b
In which:
- m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.
- b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.
The road connects points (–3, 7) and (8, 2), hence the slope is given by:
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.
Multiplying by 11:
11y = -5x + 62.
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 https://brainly.com/question/24342899
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