SOLUTION: Find h(k-2) if h(x)= 3x^2-5x+1 Thank you so much for your help!

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Question 667470: Find h(k-2) if h(x)= 3x^2-5x+1
Thank you so much for your help!
Answer by jerryguo41(197) About Me  (Show Source):
You can put this solution on YOUR website!
h%28k-2%29=+3x%5E2-5x%2B1
h%28k-2%29=+3%28k-2%29%5E2-5%28k-2%29%2B1
h%28k-2%29=+3%28k%5E2-4k%2B4%29-5k%2B10%2B1
h%28k-2%29=+3k%5E2-12k%2B12-5k%2B11
h%28k-2%29=+3k%5E2-17k%2B23
if h(K-2)=0 then:
0=+3k%5E2-17k%2B23
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ak%5E2%2Bbk%2Bc=0 (in our case 3k%5E2%2B-17k%2B23+=+0) has the following solutons:

k%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=%28-17%29%5E2-4%2A3%2A23=13.

Discriminant d=13 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--17%2B-sqrt%28+13+%29%29%2F2%5Ca.

k%5B1%5D+=+%28-%28-17%29%2Bsqrt%28+13+%29%29%2F2%5C3+=+3.43425854591066
k%5B2%5D+=+%28-%28-17%29-sqrt%28+13+%29%29%2F2%5C3+=+2.232408120756

Quadratic expression 3k%5E2%2B-17k%2B23 can be factored:
3k%5E2%2B-17k%2B23+=+3%28k-3.43425854591066%29%2A%28k-2.232408120756%29
Again, the answer is: 3.43425854591066, 2.232408120756. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+3%2Ax%5E2%2B-17%2Ax%2B23+%29