SOLUTION: I need help with these problems Solve by using the quadratic formula: 3x^2=11x+4 and also find the axis of symmetry: y=-x^2+4x+2 Thanks a million

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: I need help with these problems Solve by using the quadratic formula: 3x^2=11x+4 and also find the axis of symmetry: y=-x^2+4x+2 Thanks a million      Log On


   

Question 93122: I need help with these problems
Solve by using the quadratic formula: 3x^2=11x+4


and also find the axis of symmetry: y=-x^2+4x+2


Thanks a million
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
1) Solve using the quadratic formula:x+=+%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F2a
3x%5E2+=+11x%2B4
First, write the equation in standard form for quadratic equations:
ax%5E2%2Bbx%2Bc+=+0
3x%5E2-11x-4+=+0 Here, you can see that: a = 3, b = -11, and c = -4
Make the appropriate substitutions into the formula and solve for x:
x+=+%28-%28-11%29%2B-sqrt%28%28-11%29%5E2-4%283%29%28-4%29%29%29%2F2%283%29 Simplify this.
x+=+%2811%2B-sqrt%28121-%28-48%29%29%29%2F6
x+=+%2811%2B-sqrt%28169%29%29%2F6
x+=+%2811%2B13%29%2F6 or x+=+%2811-13%29%2F6
x+=+24%2F6 or x+=+-2%2F6
x+=+4 or x+=+-1%2F3
2) Find the axis of symmetry for:
y+=+-x%5E2%2B4x%2B2
The axis of symmetry is given by:
x+=+%28-b%29%2F4a
Your equation here is already in standard form:y+=+ax%5E2%2Bbx%2Bc so a = -1, b = 4, and c = 2
The axis of symmetry is:
x+=+%28-4%29%2F2%28-1%29
x+=+%28-4%29%2F%28-2%29
x+=+2 This is the equation of axis of symmetry!