The equation for the line of symmetry for the quadratic function
[f(x) = (14+6x-3x²)] will be (x = 1).
As per the question statement, we are provided with a quadratic function [f(x) = (14+6x-3x²)].
We are required to determine the line of symmetry for the above-mentioned quadratic function.
To solve this question, we need to know about the relation between a standard quadratic equation of parabola and it's line or axis of symmetry.
The Standard quadratic equation of a parabola goes as [tex][y=f(x)=(ax^{2} +bx+c)][/tex] and axis of symmetry is [tex](x=\frac{-b}{2a})[/tex].
Here, we will have to compare our question mentioned quadratic function with the above-mentioned standard quadratic form of parabola, and identify the "a" and "b" values, and then use these values in the form of above-mentioned axis of symmetry, to obtain our desired a answer.
Comparing [tex](14+6x-3x^{2} )[/tex] and [tex](ax^{2} +bx+c)[/tex], we can identify [a = -(3)] and (b = 6). Therefore, axis of symmetry for the quadratic function
[f(x) = (14+6x-3x²)] will be
[tex][x=\frac{-6}{2*(-3)}]\\or,[x=\frac{-6}{-6}]\\ or,(x=1)[/tex]
- Axis of Symmetry: In mathematics, an object is said to be symmetric if it can be divided into two identical halves and the line or axis that divides the object into its identical halves is called the line of symmetry.
To learn more about Axis of Symmetry, click on the link below.
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