Question

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

Answer 1

Answer:

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  

Step-by-step explanation:

Answer 2

Answer:

The given function is

$f(x)=\frac{1}{2}x^{2} +2x-6$

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

$\frac{1}{2}x^{2} +2x-6=0\\2(\frac{1}{2}x^{2} +2x-6)=2(0)\\x^{2}+4x-12=0\\(x+6)(x-2)=0\\x=-6\\x=2$

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

$x=\frac{-b}{2a}=\frac{-2}{2(\frac{1}{2}) }=-2$

The vertical coordinate of the vertex is

$f(-2)=\frac{1}{2}(-2)^{2}+2(-2)-6=2-4-6=-8$

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

The graph would be as the image attached.