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

Algebra ->  Quadratic Equations and Parabolas -> 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      Log On


   

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) About Me  (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

0=x%5E2-4x-21


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


Starting with the general quadratic

ax%5E2%2Bbx%2Bc=0

the general solution using the quadratic equation is:

x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29



So lets solve x%5E2-4%2Ax-21=0 ( notice a=1, b=-4, and c=-21)




x+=+%28--4+%2B-+sqrt%28+%28-4%29%5E2-4%2A1%2A-21+%29%29%2F%282%2A1%29 Plug in a=1, b=-4, and c=-21



x+=+%284+%2B-+sqrt%28+%28-4%29%5E2-4%2A1%2A-21+%29%29%2F%282%2A1%29 Negate -4 to get 4



x+=+%284+%2B-+sqrt%28+16-4%2A1%2A-21+%29%29%2F%282%2A1%29 Square -4 to get 16 (note: remember when you square -4, you must square the negative as well. This is because %28-4%29%5E2=-4%2A-4=16.)



x+=+%284+%2B-+sqrt%28+16%2B84+%29%29%2F%282%2A1%29 Multiply -4%2A-21%2A1 to get 84



x+=+%284+%2B-+sqrt%28+100+%29%29%2F%282%2A1%29 Combine like terms in the radicand (everything under the square root)



x+=+%284+%2B-+10%29%2F%282%2A1%29 Simplify the square root (note: If you need help with simplifying the square root, check out this solver)



x+=+%284+%2B-+10%29%2F2 Multiply 2 and 1 to get 2

So now the expression breaks down into two parts

x+=+%284+%2B+10%29%2F2 or x+=+%284+-+10%29%2F2

Lets look at the first part:

x=%284+%2B+10%29%2F2

x=14%2F2 Add the terms in the numerator
x=7 Divide

So one answer is
x=7



Now lets look at the second part:

x=%284+-+10%29%2F2

x=-6%2F2 Subtract the terms in the numerator
x=-3 Divide

So another answer is
x=-3

So our solutions are:
x=7 or x=-3

Notice when we graph x%5E2-4%2Ax-21, we get:

+graph%28+500%2C+500%2C+-13%2C+17%2C+-13%2C+17%2C1%2Ax%5E2%2B-4%2Ax%2B-21%29+

and we can see that the roots are x=7 and x=-3. This verifies our answer


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