Answer:
The vertex of this parabola is [tex](-2,-11)[/tex]
Step-by-step explanation:
One way of finding the x-coordinate of the vertex of a parabola is by using the equation [tex]-\frac{b}{2a}[/tex]
From the function [tex]f(x)=x^2+4x-7[/tex], we can see that
[tex]a=1\\b=4\\c=-7[/tex]
This means that
[tex]-\frac{b}{2a}=-\frac{4}{2(1)} =-2[/tex]
So, the x-value of the vertex is -2. Now, we can plug this x-value into the function to find the y-coordinate of the point.
[tex]f(x)=x^2+4x-7\\\\f(-2)=(-2)^2+4(-2)-7\\\\f(-2)= 4-8-7\\\\f(-2)=-11[/tex]
Thus, the vertex of this parabola is [tex](-2,-11)[/tex]
