SOLUTION: I am having problems finding the vertex of this problem.. could someone please help. Problem : Consider the Quadratic function f(x)=4x^2-64. Its vertex is ( ? , ?) Its x

Algebra ->  Functions -> SOLUTION: I am having problems finding the vertex of this problem.. could someone please help. Problem : Consider the Quadratic function f(x)=4x^2-64. Its vertex is ( ? , ?) Its x      Log On


   

Question 189666: I am having problems finding the vertex of this problem.. could someone please help.
Problem : Consider the Quadratic function f(x)=4x^2-64. Its vertex is ( ? , ?) Its x-intercepts are x= (?,?) Its y- intercept is y= ?
How do you find the vertex from an equation like this, I know the formula f(x) = (x-h)^2+k plays a part but I am not sure how it relates to the equation.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

Vertex:



In order to find the vertex, we first need to find the x-coordinate of the vertex.


To find the x-coordinate of the vertex, use this formula: x=%28-b%29%2F%282a%29.


x=%28-b%29%2F%282a%29 Start with the given formula.


From y=4x%5E2-64, we can see that a=4, b=0, and c=-64.


x=%28-%280%29%29%2F%282%284%29%29 Plug in a=4 and b=0.


x=%280%29%2F%288%29 Multiply 2 and 4 to get 8.


x=0 Divide.


So the x-coordinate of the vertex is x=0. Note: this means that the axis of symmetry is also x=0.


Now that we know the x-coordinate of the vertex, we can use it to find the y-coordinate of the vertex.


y=4x%5E2-64 Start with the given equation.


y=4%280%29%5E2-64 Plug in x=0.


y=4%280%29-64 Square 0 to get 0.


y=0-64 Multiply 4 and 0 to get 0.


y=-64 Combine like terms.


So the y-coordinate of the vertex is y=-64.


So the vertex is .



X-Intercept(s):




Remember, the x-intercepts occur when y=0


y=4x%5E2-64 Start with the given equation.


0=4x%5E2-64 Plug in y=0.


Notice we have a quadratic equation in the form of ax%5E2%2Bbx%2Bc where a=4, b=0, and c=-64


Let's use the quadratic formula to solve for x


x+=+%28-b+%2B-+sqrt%28+b%5E2-4ac+%29%29%2F%282a%29 Start with the quadratic formula


x+=+%28-%280%29+%2B-+sqrt%28+%280%29%5E2-4%284%29%28-64%29+%29%29%2F%282%284%29%29 Plug in a=4, b=0, and c=-64


x+=+%280+%2B-+sqrt%28+0-4%284%29%28-64%29+%29%29%2F%282%284%29%29 Square 0 to get 0.


x+=+%280+%2B-+sqrt%28+0--1024+%29%29%2F%282%284%29%29 Multiply 4%284%29%28-64%29 to get -1024


x+=+%280+%2B-+sqrt%28+0%2B1024+%29%29%2F%282%284%29%29 Rewrite sqrt%280--1024%29 as sqrt%280%2B1024%29


x+=+%280+%2B-+sqrt%28+1024+%29%29%2F%282%284%29%29 Add 0 to 1024 to get 1024


x+=+%280+%2B-+sqrt%28+1024+%29%29%2F%288%29 Multiply 2 and 4 to get 8.


x+=+%280+%2B-+32%29%2F%288%29 Take the square root of 1024 to get 32.


x+=+%280+%2B+32%29%2F%288%29 or x+=+%280+-+32%29%2F%288%29 Break up the expression.


x+=+%2832%29%2F%288%29 or x+=++%28-32%29%2F%288%29 Combine like terms.


x+=+4 or x+=+-4 Simplify.


So the answers are x+=+4 or x+=+-4


This means that the x-intercepts are (4,0) and (-4,0)




Y-Intercept:





Remember, the y-intercept occurs when x=0


y=4x%5E2-64 Start with the given equation.


y=4%280%29%5E2-64 Plug in x=0.


y=4%280%29-64 Square 0 to get 0.


y=0-64 Multiply 4 and 0 to get 0.


y=-64 Combine like terms.


So the y-intercept is (0,-64)