SOLUTION: Find the x-intercepts. y = x^2 - 4x - 32

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Question 173630This question is from textbook Introductory Algebra
: Find the x-intercepts.
y = x^2 - 4x - 32 This question is from textbook Introductory Algebra

Found 2 solutions by vleith, jojo14344:
Answer by vleith(2983) About Me  (Show Source):
You can put this solution on YOUR website!
y+=+x%5E2+-+4x+-+32
To find x-intecepts, set y=0
0+=+x%5E2+-+4x+-+32
0+=+%28x-8%29%28x%2B4%29
x = 8 and x = -4
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-4x%2B-32+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%28-4%29%5E2-4%2A1%2A-32=144.

Discriminant d=144 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--4%2B-sqrt%28+144+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-4%29%2Bsqrt%28+144+%29%29%2F2%5C1+=+8
x%5B2%5D+=+%28-%28-4%29-sqrt%28+144+%29%29%2F2%5C1+=+-4

Quadratic expression 1x%5E2%2B-4x%2B-32 can be factored:
1x%5E2%2B-4x%2B-32+=+1%28x-8%29%2A%28x--4%29
Again, the answer is: 8, -4. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-4%2Ax%2B-32+%29

See this URL for a tool to help you with this stuff
http://www.algebra.com/algebra/homework/quadratic/quadratic.solver

Answer by jojo14344(1513) About Me  (Show Source):
You can put this solution on YOUR website!

y+=+x%5E2+-+4x+-+32
Continue solving by Quadratic Eqn:
where----->system%28a=1%2Cb=-4%2Cc=-32%29
x=%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F%282a%29
x=%28-%28-4%29%2B-sqrt%28-4%5E2-4%2A1%2A-32%29%29%2F%282%2A1%29
x=%284%2B-sqrt%2816%2B128%29%29%2F2=%284%2B-sqrt%28144%29%29%2F2=%284%2B-12%29%2F2
x=%284%2B12%29%2F2=16%2F2
highlight%28x=8%29
x=%284-12%29%2F2=-8%2F2
highlight%28x=-4%29
See graph:

Thank you,
Jojo