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.Com
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) (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
If no mistake were made, then that standard form equation says (2,-6) is the vertex, axis of symmetry is , the range for y is .
Also, y-intercept at y=6.
Answer by MathLover1(20850) (Show Source): You can put this solution on YOUR website!
for
a.find the values of the intercepts
...since ,then we need to find for what is
..........use quadratic formula
solutions
-exact solution or approximately
or
or approximately
b.state the coordinates of the intercept
set to find the intercept
the intercept is at (,)
c.state the vertex
the equation for a parabola can also be written in "vertex form":
In this equation, the vertex of the parabola is the point (,).
...complete square
=> and
so, (,)=(,)
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
e.state the direction of the parabola
since and if , the parabola opens
f.decide whether there is a relative maximum or minimum, then state it
the parabola opens have an minimum
g.graph the function accurately using the above information
h. state the domain
(all real numbers)
i.state the range
{ element : }
j.state the interval of where the graph is increasing
(,)
k.state the interval of where the graph is decreasing
(,)
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