Question

F(x)=x²+4x-7 determine the vertex

Answer 1

The vertex of this parabola is
`(-2,-11)`

Explanation:

One way of finding the x-coordinate of the vertex of a parabola is by using the equation
`-(b)/(2a)`

From the function
`f(x)=x^2+4x-7`, we can see that

`a=1\\b=4\\c=-7`

This means that

`-(b)/(2a)=-(4)/(2(1)) =-2`

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.

`f(x)=x^2+4x-7\\\\f(-2)=(-2)^2+4(-2)-7\\\\f(-2)= 4-8-7\\\\f(-2)=-11`

Thus, the vertex of this parabola is
`(-2,-11)`