Question

Which is the graph of the function f(x) = x2 + 2x – 6? Mark this and return

Answer 1

Vertex: ( -1, -7 )

Focus: ( -1, -27/4 )

Axis of Symmetry: x = -1

Directrix: y = -29/4


X | Y
———
-3| -3
-2| -6
-1 | -7
0 | -6
1 | -3

Answer 2

Answer:

The graph of the function is shown below.

Step-by-step explanation:

The given function is

$f(x)=x^2+2x-6$

$f(x)=(x^2+2x)-6$

If an expression is defined as $x^2+bx$, then we need to add $(\frac{b}{2})^2$ to make it perfect square.

Here, b=2 so add and subtract 1 in the above parenthesis.

$f(x)=(x^2+2x+1-1)-6$

$f(x)=(x^2+2x+1)-1-6$

$f(x)=(x+1)^2-7$         .... (1)

The vertex form of a parabola is

$f(x)=(x-h)^2+k$      .... (2)

where, (h,k) is vertex.

On comparing (1) and (2) we get

$h=-1,k=-7$

So, the vertex of the parabola is (-1,-7) and axis of symmetry is x=-1.

The x-intercepts of the equation is

$0=(x+1)^2-7$

$7=(x+1)^2$

$\pm \sqrt{7}=x+1$

$-1\pm \sqrt{7}=x$

$x=-3.646,1.646$

Therefore, the x-intercepts are -3.646 and 1.646. The graph is shown below.