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:
The given function is
[tex]f(x)=\frac{1}{2}x^{2} +2x-6[/tex]
First, we need to find the zeros of the quadratic function, which represent the interception with the x-axis:
[tex]\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[/tex]
So, the graph of this function has two interception points with x-axis, which are [tex](-6,0);(2,0)[/tex]
Now, we have to find the vertex of the function to draw it:
The horizontal coordinate of the vertex is
[tex]x=\frac{-b}{2a}=\frac{-2}{2(\frac{1}{2}) }=-2[/tex]
The vertical coordinate of the vertex is
[tex]f(-2)=\frac{1}{2}(-2)^{2}+2(-2)-6=2-4-6=-8[/tex]
So, the vertex is at [tex](-2;-8)[/tex]
The graph would be as the image attached.
