SOLUTION: I am having problems finding the x-intercepts of the following problem. Problem : Consider the Quadratic Function of f(x)= x^2-4x-32. Its vertex is ( ?, ?) its x-intercepts a

Algebra ->  Functions -> SOLUTION: I am having problems finding the x-intercepts of the following problem. Problem : Consider the Quadratic Function of f(x)= x^2-4x-32. Its vertex is ( ?, ?) its x-intercepts a      Log On


   

Question 189673: I am having problems finding the x-intercepts of the following problem.
Problem : Consider the Quadratic Function of f(x)= x^2-4x-32. Its vertex is ( ?, ?) its x-intercepts are (?,?) , its y-intercept is (?)
Ok, I figured out the vertex of the problem which are ( 2,-36) and the y-intercept which is (-32) but I am not sure how to get the x-intercepts. Could someone please help me?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
X-Intercept(s):


Remember, the x-intercept(s) occur when f(x) (or y) is equal to zero.



f%28x%29=+x%5E2-4x-32 Start with the given function.


0=+x%5E2-4x-32 Plug in f%28x%29=0


Notice we have a quadratic equation in the form of ax%5E2%2Bbx%2Bc where a=1, b=-4, and c=-32


Let's use the quadratic formula to solve for x


x+=+%28-b+%2B-+sqrt%28+b%5E2-4ac+%29%29%2F%282a%29 Start with the quadratic formula


x+=+%28-%28-4%29+%2B-+sqrt%28+%28-4%29%5E2-4%281%29%28-32%29+%29%29%2F%282%281%29%29 Plug in a=1, b=-4, and c=-32


x+=+%284+%2B-+sqrt%28+%28-4%29%5E2-4%281%29%28-32%29+%29%29%2F%282%281%29%29 Negate -4 to get 4.


x+=+%284+%2B-+sqrt%28+16-4%281%29%28-32%29+%29%29%2F%282%281%29%29 Square -4 to get 16.


x+=+%284+%2B-+sqrt%28+16--128+%29%29%2F%282%281%29%29 Multiply 4%281%29%28-32%29 to get -128


x+=+%284+%2B-+sqrt%28+16%2B128+%29%29%2F%282%281%29%29 Rewrite sqrt%2816--128%29 as sqrt%2816%2B128%29


x+=+%284+%2B-+sqrt%28+144+%29%29%2F%282%281%29%29 Add 16 to 128 to get 144


x+=+%284+%2B-+sqrt%28+144+%29%29%2F%282%29 Multiply 2 and 1 to get 2.


x+=+%284+%2B-+12%29%2F%282%29 Take the square root of 144 to get 12.


x+=+%284+%2B+12%29%2F%282%29 or x+=+%284+-+12%29%2F%282%29 Break up the expression.


x+=+%2816%29%2F%282%29 or x+=++%28-8%29%2F%282%29 Combine like terms.


x+=+8 or x+=+-4 Simplify.


So the answers are x+=+8 or x+=+-4

This means that the x-intercepts are (8,0) and (-4,0)