The axis of symmetry of the quadratic function f is x = 1.
A quadratic equation is a polynomial which has the highest degree equal to two. It is a second-degree equation of the form ax² + bx + c = 0, where a, b, are the coefficients, c is the constant term, and x is the variable.
For the given situation,
The zeros of the quadratic function f are -3 and 5.
⇒ [tex]x=-3, x=5[/tex]
⇒ [tex](x+3)=0, (x-5)=0[/tex]
So, the function f is
[tex]y=(x+3)(x-5)[/tex]
⇒ [tex]y=x^{2} -2x-15[/tex]
Here a = 1, b = -2, c = -15.
The formula of axis of symmetry is
[tex]x=\frac{-b}{2a}[/tex]
⇒ [tex]x=\frac{-(-2)}{2(1)}[/tex]
⇒ [tex]x=1[/tex]
Hence we can conclude that the axis of symmetry of the quadratic function f is x = 1.
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