Question

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

Answer 1

Answer:

Zeros:

$x_1=-1+\sqrt{2}$

$x_2=-1-\sqrt{2}$

Interception with y-axis

$y=- 1$

Vertex:

(-1, -2)

Step-by-step 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:

$x=\frac{-b\±\sqrt{b^2-4ac}}{2a}$

In this case note that:

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

Then:

$x=\frac{-2\±\sqrt{2^2-4(1)(-1)}}{2}$

$x=\frac{-2\±\sqrt{8}}{2}$

$x=\frac{-2\±2\sqrt{2}}{2}$

$x_1=-1+\sqrt{2}$

$x_2=-1-\sqrt{2}$

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

$(-\frac{b}{2a}, f(-\frac{b}{2a}))$

Then:

$x=-\frac{2}{2*1}=-1$

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

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.