SOLUTION: given the x-intercepts of y=x^2-4x-21 a. (-3,0)and (7,0) b. (3,0) and (-4,0) c. (-7,0) and (4,0) d. No x-intercepts

Question 102586: given the x-intercepts of y=x^2-4x-21
a. (-3,0)and (7,0)
b. (3,0) and (-4,0)
c. (-7,0) and (4,0)
d. No x-intercepts
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
To find the x-intercepts, you have to let y=0 and solve for x

Let's use the quadratic formula to solve for x:

Starting with the general quadratic

the general solution using the quadratic equation is:

So lets solve ( notice , , and )

Plug in a=1, b=-4, and c=-21

Negate -4 to get 4

Square -4 to get 16 (note: remember when you square -4, you must square the negative as well. This is because .)

Multiply to get

Combine like terms in the radicand (everything under the square root)

Simplify the square root (note: If you need help with simplifying the square root, check out this solver)

Multiply 2 and 1 to get 2

So now the expression breaks down into two parts

or

Lets look at the first part:

Add the terms in the numerator
Divide

So one answer is

Now lets look at the second part:

Subtract the terms in the numerator
Divide

So another answer is

So our solutions are:
or

Notice when we graph , we get:

and we can see that the roots are and . This verifies our answer

This means the x-intercepts are (-3,0) and (7,0). So the answer is A
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