Question

Which is the graph of the function f(x) = one-halfx2 + 2x – 6?

Answer 1

1/2 x^2 + 2x - 6 = 0

(1/2 x - 1)(x + 6) = 0

zeroes are 2 and -6

so the graph intersects x axis at -6 and 2

The only one to do that is diagram A

Explanation:

Answer 2

The given function is

`f(x)=(1)/(2)x^(2) +2x-6`

First, we need to find the zeros of the quadratic function, which represent the interception with the x-axis:

`(1)/(2)x^(2) +2x-6=0\\2((1)/(2)x^(2) +2x-6)=2(0)\\x^(2)+4x-12=0\\(x+6)(x-2)=0\\x=-6\\x=2`

So, the graph of this function has two interception points with x-axis, which are
`(-6,0);(2,0)`

Now, we have to find the vertex of the function to draw it:

The horizontal coordinate of the vertex is

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

The vertical coordinate of the vertex is

`f(-2)=(1)/(2)(-2)^(2)+2(-2)-6=2-4-6=-8`

So, the vertex is at
`(-2;-8)`

The graph would be as the image attached.