Question

Describe the key features of the graph of the quadratic function f(x) = x2 + 2x - 1

Answer 1

Zeros:

`x_1=-1+√(2)`

`x_2=-1-√(2)`

Interception with y-axis

`y=- 1`

Vertex:

(-1, -2)

Explanation:

We have the following quadratic function

`f(x) = x^2 + 2x - 1`

To find the zeros of the function, make
`f(x) = 0` and solve for the variable x

`x^2 + 2x - 1=0`

We must factor the expression. Then we use the quadratic formula:

For a function of the form
`ax ^ 2 + bx + c = 0` the quadratic formula is:

`x=(-b\±√(b^2-4ac))/(2a)`

In this case note that:

`a=1\\b=2\\c=-1`

Then:

`x=(-2\±√(2^2-4(1)(-1)))/(2)`

`x=(-2\±√(8))/(2)`

`x=(-2\±2√(2))/(2)`

`x_1=-1+√(2)`

`x_2=-1-√(2)`

We know that the vertex of a quadratic function is at the point:

`(-(b)/(2a), f(-(b)/(2a)))`

Then:

`x=-(2)/(2*1)=-1`

`y=f(-1) = (-1)^2+2(-1) -1 = -2`

The vertex is: (-1, -2)

The intersection with the y-axis we find it doing
`x = 0` and solving for y

`y=f(0) = 0^2 + 2*0 - 1`

`y=- 1`

Look at the attached image.