how can you graph x2+4x-21>0?

Question

x2 is x-squared

Answer 1

You could factor it into: (x+7)(x-3)>0
Both brackets would have to be positive or both negative for the statement to be true.
To be positive: x would have to be greater than 3
To be negative: x would have to be less than -7

Answer 2

x^2 + 4x - 21 > 0

The first thing to do is factor the left hand side. It actually factors nicely, into

(x + 7) (x - 3) > 0

Now, to determine the critical values, we actually *equate* the left hand side to 0. Therefore,
(x + 7) (x - 3) = 0 implies x = {-7, 3}.

This is not the solution; they are only key values with which we will find the solution.

Now that we have these two critical values, we're going to investigate the behaviour *around* them. The three key intervals are: (-infinity, -7) , (-7, 3) , and (3, infinity).

Here's what's going to happen: we can choose ANY one value for each interval; what we want are the intervals where it is POSITIVE, given that our inequality states x^2 + 4x - 21 to be GREATER than 0.

What we're testing for positivity/negativity: (x + 7) (x - 3).

Value test for (-infinity, -7): Test -1000000. That would make
(x + 7) (x - 3) to be (negative) times (negative) = positive. So we INCLUDE the interval (-infinity, -7). {NOTE: I use round brackets instead of square brackets, because the inequality is strictly greater than 0, as opposed to greater than or equal to.}

Value test for (-7, 3): Test 0; then (x + 7) (x - 3) = (7)(-3) = -21, which is negative. Therefore, we exclude the interval (-7, 3)

Value test for (3, infinity): Test 100000000. Then we have
(x + 7) (x - 3) = (really big positive number) x (really big positive number) = positive, which is what we want. Therefore, we include the interval (3,infinity).

Therefore, the solution set to the inequality is x such that x lies in the interval (-infinity, -7) U (3, infinity).

The "U" means "union".

Answer 3

evaluate the words with "x". x^2 + 4x . finished the sq. by using including and subtracting 4. x^2 + 4x + 4 = 4 + y^2 -6y -3 = 0 (x+2)^2 + ... and so on. Do the comparable element with the y-words. you would be waiting to rearrange it right into a style (x-a)^2 + (y-b)^2 = r^2 the place the middle of the circle is (a,b), and the radius is r.

Answer 4

Draw the line y=x^2+4x-21. Then shade the area about the line

Answer 5

for a graph, go to www.quickmath.com, click on Plot under Inequalities, type in x^2 + 4x - 21 > 0, and you will get your graph.

Answer 6

(x+7)(x-3)>0
the value of x must be otside -7 and 3
x>3 x<-7
-7>x>3

Answer 7

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http://www.calc101.com/webMathematica/sketch.jsp

Answer 8

(x+7)(x-3)>0
x+7>0
x-3>0
x>-7 and 3
(-∞,-7)U(3,∞)