Respuesta :
Using it's vertex, it is found that the quadratic function with an axis of symmetry at [tex]x = \frac{1}{4}[/tex] is given by:
f(x) = 2x² - x + 1.
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]
The axis of symmetry is at [tex]x = x_v[/tex].
In this problem, considering the desired axis of symmetry, we have that:
[tex]-\frac{b}{2a} = \frac{1}{4}[/tex]
[tex]b = -\frac{a}{2}[/tex]
Hence the function is:
f(x) = 2x² - x + 1, which has a = 2, b = -1.
More can be learned about the vertex of a quadratic function at https://brainly.com/question/24737967
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