Respuesta :
The quadratic function that has a minimum located at (4,-3) is given by:
f(x) = 2x² - 16x + 35
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, the function has a minimum, which means that a > 0, eliminating the first two options. The x-value of the vertex is of x = 4, hence -b/2a = 4, which means that the function is given by:
f(x) = 2x² - 16x + 35.
More can be learned about quadratic functions at https://brainly.com/question/24737967
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