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Sagot :
Using the vertex of the quadratic equation, it is found that the maximum profit she can earn is of $106.
What is the vertex of a quadratic equation?
A quadratic equation is modeled by:
[tex]y = ax^2 + bx + c[/tex]
The vertex is given by:
[tex](x_v, y_v)[/tex]
In which:
[tex]x_v = -\frac{b}{2a}[/tex]
[tex]y_v = -\frac{b^2 - 4ac}{4a}[/tex]
Considering the coefficient a, we have that:
- If a < 0, the vertex is a maximum point.
- If a > 0, the vertex is a minimum point.
In this problem, her profit is modeled by:
[tex]P(x) = -x^2 + 14x + 57[/tex]
Which is a quadratic equation with coefficients a = -1, b = 14, c = 57, hence, her maximum profit in dollars is given by:
[tex]y_v = -\frac{14^2 - 4(-1)(57)}{4(-1)} = 106[/tex]
More can be learned about the vertex of a quadratic equation at https://brainly.com/question/24737967
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