Respuesta :
The quadratic function [tex]f(x)[/tex] has one zero at [tex]x=-5[/tex] and a turning point at [tex](3,10)[/tex]. The value of other zero is [tex]11[/tex].
What is Quadratic function?
The Quadratic function [tex]f(x)[/tex] is a polynomial function with one or more variables in which the highest power of the variable is two. i.e. [tex]f(x) = ax^{2} + bx + c[/tex]
What are zeros?
The zeros of a polynomial [tex]f(x)[/tex] are all the [tex]x[/tex]-values that make the polynomial equals to zero. i.e. [tex]f(x)=0[/tex]
What is turning point?
A turning point is a point at which the derivative changes sign.
We have,
One zero is [tex](-5)[/tex],
Let other Zero be [tex]"a"[/tex],
Turning point at [tex](3,10)[/tex].
i.e. [tex]x=3[/tex] and [tex]y=10[/tex]
Since the difference between [tex]3[/tex] and [tex](-5)[/tex] is [tex]8[/tex].
So,
The difference between the other zero from [tex]3[/tex] should be the same as the difference between [tex]3[/tex] and [tex](-5)[/tex].
i.e.
[tex]a-3=8[/tex]
[tex]a=11[/tex]
Hence the value of its other zero is [tex]11.[/tex]
To learn more about zeros click here
https://brainly.com/question/5975436
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