SOLUTION: I am trying to solve for x (to find the x intercept) in the equation y=(-1/2)x^2+2x+10. I got the y intercept (10) by "letting x=0", but when I try to do the same, "letting y=0",

Algebra ->  Graphs -> SOLUTION: I am trying to solve for x (to find the x intercept) in the equation y=(-1/2)x^2+2x+10. I got the y intercept (10) by "letting x=0", but when I try to do the same, "letting y=0",      Log On


   

Question 264395: I am trying to solve for x (to find the x intercept) in the equation
y=(-1/2)x^2+2x+10. I got the y intercept (10) by "letting x=0", but when I try to do the same, "letting y=0", I get confused due to the fraction and exponent and do not know how to isolate the x. Can someone please explain this to me. Thank you!
Found 2 solutions by richwmiller, Alan3354:
Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!

You need to use the quadratic formula to solve for x
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case -0.5x%5E2%2B2x%2B10+=+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=%282%29%5E2-4%2A-0.5%2A10=24.

Discriminant d=24 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-2%2B-sqrt%28+24+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%282%29%2Bsqrt%28+24+%29%29%2F2%5C-0.5+=+-2.89897948556636
x%5B2%5D+=+%28-%282%29-sqrt%28+24+%29%29%2F2%5C-0.5+=+6.89897948556636

Quadratic expression -0.5x%5E2%2B2x%2B10 can be factored:
-0.5x%5E2%2B2x%2B10+=+-0.5%28x--2.89897948556636%29%2A%28x-6.89897948556636%29
Again, the answer is: -2.89897948556636, 6.89897948556636. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-0.5%2Ax%5E2%2B2%2Ax%2B10+%29

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
y=(-1/2)x^2+2x+10
(-1/2)x^2+2x+10 = 0
Multiply by -2
x^2 - 4x - 20 = 0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-4x%2B-20+=+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-20=96.

Discriminant d=96 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--4%2B-sqrt%28+96+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-4%29%2Bsqrt%28+96+%29%29%2F2%5C1+=+6.89897948556636
x%5B2%5D+=+%28-%28-4%29-sqrt%28+96+%29%29%2F2%5C1+=+-2.89897948556636

Quadratic expression 1x%5E2%2B-4x%2B-20 can be factored:
1x%5E2%2B-4x%2B-20+=+%28x-6.89897948556636%29%2A%28x--2.89897948556636%29
Again, the answer is: 6.89897948556636, -2.89897948556636. 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-20+%29

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x = 2 +/- 2sqrt(3)