SOLUTION: for g(x)=3x^2-12x+6 a,find the values of the x intercepts b,state the coordinates of the y intercept c,state the vertex d,state the axis of symmetry e,state the direction of t

Algebra ->  Functions -> SOLUTION: for g(x)=3x^2-12x+6 a,find the values of the x intercepts b,state the coordinates of the y intercept c,state the vertex d,state the axis of symmetry e,state the direction of t      Log On


   

Question 959744: for g(x)=3x^2-12x+6
a,find the values of the x intercepts
b,state the coordinates of the y intercept
c,state the vertex
d,state the axis of symmetry
e,state the direction of the parabola
f,decide whether there is a relative maximum or minimum, then state it
g,graph the function accurately using the above information
h, state the domain
i,state the range
j,state the interval of x where the graph is increasing
k,state the interval of x where the graph is decreasing
Found 2 solutions by josgarithmetic, MathLover1:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
That is a parabola with a minimum, vertical axis of symmetry, and domain is all real numbers. Other details you find through Completing The Square, as in this lesson: http://www.algebra.com/my/Completing-the-Square-to-Solve-General-Quadratic-Equation.lesson?content_action=show_dev

y=3%28x%5E2-4x%2B2%29
y=3%28x%5E2-4x%2B4%2B2-4%29
y=3%28%28x-2%29%5E2-2%29
highlight%28y=3%28x-2%29%5E2-6%29

If no mistake were made, then that standard form equation says (2,-6) is the vertex, axis of symmetry is x=2, the range for y is y%3E=-6.
Also, y-intercept at y=6.

graph%28300%2C300%2C-10%2C10%2C-10%2C10%2C3%28x-2%29%5E2-6%29

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
for g%28x%29=3x%5E2-12x%2B6
a.find the values of the x intercepts
3x%5E2-12x%2B6=0
3%28x%5E2-4x%2B2%29=0...since 3%3C%3E0,then we need to find for what x is
%28x%5E2-4x%2B2%29=0..........use quadratic formula
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
x+=+%28-%28-4%29+%2B-+sqrt%28+%28-4%29%5E2-4%2A1%2A2+%29%29%2F%282%2A1%29+
x+=+%284+%2B-+sqrt%28+16-8+%29%29%2F2+
x+=+%284+%2B-+sqrt%28+8+%29%29%2F2+

x+=+%28cross%284%292+%2B-+cross%282%29sqrt%282+%29%29%2Fcross%282%29+
x+=+%282+%2B-+sqrt%282+%29%29+
solutions
x+=+2+%2Bsqrt%28+2+%29+-exact solution or x+=+3.41+ approximately
or
x+=+2+-sqrt%28+2+%29+ or x+=+0.59+ approximately
b.state the coordinates of the y intercept
set x=0 to find the y intercept
y=3%2A0%5E2-12%2A0%2B6
y=6
the y intercept is at (0,6)

c.state the vertex
the equation for a parabola can also be written in "vertex form":
y+=+a%28x+-+h%29%5E2+%2B+k
In this equation, the vertex of the parabola is the point (h,+k).
y=%283x%5E2-12x%29%2B6...complete square
y=3%28x%5E2-4x%2B_%29-3%2A_%2B6
y=3%28x%5E2-4x%2B2%5E2%29-3%2A2%5E2%2B6
y=3%28x-2%29%5E2-12%2B6
y=3%28x-2%29%5E2-6+=> h=2 and k=-6
so, (h,+k)=(2,+-6)
d.state the axis of symmetry
The line that passes through the vertex and divides the parabola into two symmetric parts is called the axis of symmetry.
here, that is x=2
e.state the direction of the parabola
since a=3 and if +a+%3E+0, the parabola opens upward

f.decide whether there is a relative maximum or minimum, then state it
the parabola opens upward have an minimum

g.graph the function accurately using the above information


h. state the domain
R (all real numbers)
i.state the range
{ y element R : y%3E=-6 }
j.state the interval of x where the graph is increasing
(2,infinity)
k.state the interval of x where the graph is decreasing
(-infinity,2)