Given the function f(x)=3x^2+24x-2 find the following

Question

find the vertex of the graph of f(x).

 

find the x-intercepts if any.

 

find the maximum value obtained by f(x).

 

find the minimum value obtained by f(x).

Answer 1

Porsha, let's take a look.

 

First, the vertex.  To find x for the vertex, we use -b/2a, soooo we plug in -24/2(3) = -24/6 = -4.

 

Now that we have a value for x, we plug it in and find y.  3(-4)² + 24(-4) - 2 = 3(16) - 96 - 2 = 48 - 96 - 2 = -50

 

So, our vertex is (-4, -50).  Because "a" is positive, we know that the function opens up and, therefore, has a minimum. The minimum is the lowest it goes, so the answer is y = -50

 

For x-intercepts, we set the function equal to 0, since y = 0 all along the x-axis.

 

So, 3x² + 24x - 2 = 0.  This doesn't seem to factor, so we are going to have to use the quadratic formula.

 

-b +√b² - 4ac   = -24 +  √24² - 4(3)(-2)  = -24 + √576 + 24  = -24 + √600  

____________     __________________      ______________     __________     

 

    2a                            2(3)                              6                        6  

 

 

Plug both into your calculator ( + and -) for your answers, which will be written as x = something and x = something.

 

The maximum value is infinity.

 

Hope this helps!