Question

Find the x-intercepts for the parabola defined by the equation below.

Answer 1

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:

$2x^2+4x-2x-4=0$

Now group the terms in sets of 2 without moving any of them around:

$(2x^2+4x)-(2x-4)=0$

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:

$2x(x+2)-2(x+2)$

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:

$(x+2)(2x-2)=0$

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)