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

y= 2^2 + 2x - 4

a. -4,0 and 2,0
b. -2,0 and 1,0
c. 0,-2 and 0,1
d. 0,-4 and 0,2

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:

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

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:

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:

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)

step-by-step explanation:

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- "runner b is moving at a slower rate."

- "the graphs shown are graphs of distance(km) against time(min).

the slopes of this graphs are are given by:

slope = (change in y)/(change in x)

= (change in distance)/(change in time)

this is the formula for finding the speed. so, the slope of these graphs represent the speed of the runner.

taking each division in the graph to represent 1 on both axis:

runner a ⇒ speed = (2-0)/(1-0)

= 2/1

= 2 km/min

runner b ⇒ speed = (3-0)/(3-0)

= 3/3

= 1 km/min

this shows that   runner b is moving at a slower rate."