SOLUTION: apply the quadratic formula to find the roots of the given function, and then graph the function. f(x) = x^2 + 4 g(x) = x^2 + x + 12

Algebra ->  Square-cubic-other-roots -> SOLUTION: apply the quadratic formula to find the roots of the given function, and then graph the function. f(x) = x^2 + 4 g(x) = x^2 + x + 12       Log On


   

Question 48578: apply the quadratic formula to find the roots of the given function, and then graph the function.
f(x) = x^2 + 4

g(x) = x^2 + x + 12
Found 2 solutions by venugopalramana, tutorcecilia:
Answer by venugopalramana(3286) About Me  (Show Source):
You can put this solution on YOUR website!
apply the quadratic formula to find the roots of the given function, and then graph the function.
f(x) = x^2 + 4
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
x+=+%280+%2B-+sqrt%28+0-4%2A1%2A4+%29%29%2F%282%2A1%29+
x+=+%280%2B-+sqrt%28+-4+%29%29%2F%282%29+
X=+i....OR......-i
X..........0...............1..............2........ETC
Y..........0...............5..............8.........ETC
+graph%28+500%2C+500%2C+-10%2C+100%2C+-10%2C+100%2Cx%5E2%2B4%29+
g(x) = x^2 + x + 12
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
x+=+%28-1+%2B-+sqrt%28+1%5E2-4%2A1%2A12+%29%29%2F%282%2A1%29+
x+=+%28-1+%2B-+sqrt%28+1-48+%29%29%2F%282%29+
x+=+%28-1+%2B-+sqrt%2847%29%29%2F%282%29+
X=-0.5+i*0.5*SQRT(47)............OR..........-0.5-i*0.5*SQRT(47)
X..0..........1.........2.......ETC
Y..12.........14........18.ETC
+graph%28+500%2C+500%2C+-5%2C+100%2C+-5%2C+100%2Cx%5E2%2Bx%2B12%29+

Answer by tutorcecilia(2152) About Me  (Show Source):
You can put this solution on YOUR website!
f(x) = x^2 + 4
Let:
a=1
b=0
c=4
.
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+ [Plug-in the values]
.
x+=+%28-0+%2B-+sqrt%28+0%5E2-4%281%29%284%29+%29%29%2F%282%281%29%29+
x+=+%28-0+%2B-+sqrt%28+-16%29+%29%29%2F%282%29%29+ [Simplify]
x+=+%28-0+%2B-+4i%29%2F2+%29%29%29+[Cancel out]
x = +-2i [x = -2i or x = +2i] [Final answers]
.

+graph%28+300%2C+200%2C+-5%2C+6%2C+-5%2C+10%2C+x%5E2+%2B+4%29+
.
.


g(x) = x^2 + x + 12
Let:
a = 1
b = 1
c = 12
.
.
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
.
x+=+%28-1+%2B-+sqrt%28+1%5E2-4%281%29%2812%29+%29%29%2F%282%281%29%29+
.
x+=+%28-1+%2B-+sqrt%28+-47%29+%29%29%2F%282%29+
.
x+=+%28-1%2F2+%2B-+%28+-47%2F2%29+%29%29+
.
x+=+%28%28-1%2F2%29+%2B-+%2847i%2F2%29%29
.
.
+graph%28+400%2C+400%2C+-13%2C+13%2C+-2%2C+25%2C+x%5E2+%2B+x+%2B+12+%29+