Math Homework help

Question

Given y=x^2-4x-21 find each of the following

y-intercept

x-intercept

coordinates of vertex

is the parabola max or min value

the max or min value

Answer 1

For the y-intercept, plug 0 in for x:

y = 0²-4(4)-21=-21 --> (0,-21) for y-intercept

 

For x-intercepts, factor the equation, and set equal to zero

y = x²-4x-21

   = (x-7)(x+3) = 0

   --> x=7 or x=-3

   --> (7,0) and (-3,0) for x-intercepts

 

For the vertex, since we have just found the x-intercepts, we can use the average of the x-values, since the vertex will be exactly half way between the x-intercepts.  Lets call the vertex (h,k).

 

h = (-3+7)/2 = 4/2 = 2.  Now plus this value into the equation to get k:

k= (2)²-4(2)-21 = -25.

--> vertex is (2,-25)

 

For whether the function has a min or max, it has a min, since the coefficient of the x² term is +1 (positive, in particular).

 

What is the minimum value?  This would be the 'k' value = -25.