For each function, (a) determine whether the graph opens upward or downward,
(b) find the axis of symmetry, (c) find the vertex, (d) find the y-intercept, and
(e) graph the function. g(x) = -3x^2 + 6x

Question

For each function, (a) determine whether the graph opens upward or downward,
(b) find the axis of symmetry, (c) find the vertex, (d) find the y-intercept, and
(e) graph the function.  g(x) = -3x^2 + 6x

mathmale · Answer

g(x) = -3x^2 + 6x is a quadratic function of the form y=ax^2+bx+c.  Here, a=-3, b=6 and c=0.  Because the first coefficient (a=-3) is negative, the graph of this quadratic, a parabola, opens DOWN.  

If you want to use a calculus approach, find the derivative  of  g(x) = -3x^2 + 6x, and then the 2nd derivative.

You will find that the 2nd derivative is negative.  If the 2nd deriv. of a function is neg., that means that the graph of the function at and near certain x values opens DOWN.

Setting calculus aside for now, focus on the other questions.

How would you find the axis of symmetry?  Using the coefficients a=-3 and b=6, find 
x=-b/(2a).

How would you then find the coordinates of the vertex?  Hint:  the x-coordinate is the same as that of the axis of symmetry.

Please show all work on which you want commentary.

mathmale · Answer

A hearty welcome to OpenStudy!