The coordinates of the vertex of the function
is
(-5, -28).
It is given that the function ![\rm f(x) = x^2+10x-3](https://tex.z-dn.net/?f=%5Crm%20f%28x%29%20%3D%20x%5E2%2B10x-3)
It is required to find the coordinates of the vertex.
<h3>What is a parabola?</h3>
It is defined as the graph of a quadratic function that has something bowl-shaped.
We have a function:
![\rm f(x) = x^2+10x-3](https://tex.z-dn.net/?f=%5Crm%20f%28x%29%20%3D%20x%5E2%2B10x-3)
This function represents a parabola.
We know the standard form of parabola in quadratic style:
![\rm f(x)=ax^2+bx+c](https://tex.z-dn.net/?f=%5Crm%20f%28x%29%3Dax%5E2%2Bbx%2Bc)
By comparing the given function to the standard form of parabola, we get
a = 1, b = 10, and c = -3
The vertex of the parabola is given by:
Putting the values in the above equation, we get:
![\rm x = -\frac{10}{2\times1} \Rightarrow -5](https://tex.z-dn.net/?f=%5Crm%20x%20%3D%20-%5Cfrac%7B10%7D%7B2%5Ctimes1%7D%20%5CRightarrow%20-5)
x = -5 put this value in the given parabola function, we get:
![\rm f(-5) = (-5)^2+10(-5)-3\\\rm f(-5) = 25-50-3\\\rm f(-5) = -28](https://tex.z-dn.net/?f=%5Crm%20f%28-5%29%20%3D%20%28-5%29%5E2%2B10%28-5%29-3%5C%5C%5Crm%20f%28-5%29%20%3D%2025-50-3%5C%5C%5Crm%20f%28-5%29%20%3D%20-28)
or y = -28
The coordintes = (x, y) : (-5 , -28) which is shown in the graph.
Thus, the coordinates of the vertex of the function
is (-5, -28).
Know more about the parabola here:
brainly.com/question/8708520