Answer:
b.
Step-by-step explanation:
x-intercepts are found by factoring. We will use standard factoring here since this one is straightforeward and has real zeros as its solutions.
In our equation,
a = 2
b = 2
c = -4
The rules are to take a * c and then find the factors that number, determine which combination of those factors will give you the linear term (the term with the single x on it), and rearrange those signs accordingly. Let's start with that:
Our a * c is 2 * -4 = -8.
We need the factors of |-8|: 1,8 and 2,4
Some combination of those factors needs to give us a +2x. 2,4 will work as long as the 4 is positive and the 2 is negative.
Now we put them back into the equation, the absolute value of the larger number first:
[tex]2x^2+4x-2x-4=0[/tex]
Now group the terms in sets of 2 without moving any of them around:
[tex](2x^2+4x)-(2x-4)=0[/tex]
In each set of parenthesis, pull out what is common to both terms. In the first set, the 2x is common, and in the second set, the 2 is common:
[tex]2x(x+2)-2(x+2)[/tex]
Now what is common between both terms is the (x + 2), so pull that out, grouping what is remaining in its own set of parenthesis:
[tex](x+2)(2x-2)=0[/tex]
To find the zeros, remember that the Zero Product Property tells us that for that equation above to equal zero, one of those factors has to equal zero, so:
x + 2 = 0 or 2x - 2 = 0. Solve both for x:
x = -2 so the coordinate is (-2, 0)
2x - 2 = 0 and
2x = 2 so
x = 1 so the coordinate is (1, 0)
