SOLUTION: I need help with this equations: 1) write y=4x^2-32x+66 in vertex form 2)use the quadratic formula to solve the equation 4x^2-x+3=0

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons -> SOLUTION: I need help with this equations: 1) write y=4x^2-32x+66 in vertex form 2)use the quadratic formula to solve the equation 4x^2-x+3=0      Log On


   

Question 580183: I need help with this equations:
1) write y=4x^2-32x+66 in vertex form
2)use the quadratic formula to solve the equation
4x^2-x+3=0
Answer by dfrazzetto(283) About Me  (Show Source):
You can put this solution on YOUR website!
1) write y=4x^2-32x+66 in vertex form
Complete the square:
y= 4x^-32x+64 + 66 - 64
y= (2x-8)^2 + 2
vertex = 4,2
+graph%28+300%2C+300%2C+-6%2C+5%2C+-10%2C+10%2C+4x%5E2-32x%2B66%29+
2)use the quadratic formula to solve the equation
4x^2-x+3=0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 4x%5E2%2B-1x%2B3+=+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=%28-1%29%5E2-4%2A4%2A3=-47.

The discriminant -47 is less than zero. That means that there are no solutions among real numbers.

If you are a student of advanced school algebra and are aware about imaginary numbers, read on.


In the field of imaginary numbers, the square root of -47 is + or - sqrt%28+47%29+=+6.85565460040104.

The solution is

Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+4%2Ax%5E2%2B-1%2Ax%2B3+%29