SOLUTION: Find the vertex of y=x^+4x-5 Give the coordinates of x and y

Algebra ->  Graphs -> SOLUTION: Find the vertex of y=x^+4x-5 Give the coordinates of x and y      Log On


   

Question 187594: Find the vertex of y=x^+4x-5
Give the coordinates of x and y
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
I'm assuming that the equation is y=x%5E2%2B4x-5


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=x%5E2%2B4x-5, we can see that a=1, b=4, and c=-5.


x=%28-%284%29%29%2F%282%281%29%29 Plug in a=1 and b=4.


x=%28-4%29%2F%282%29 Multiply 2 and 1 to get 2.


x=-2 Divide.


So the x-coordinate of the vertex is x=-2. Note: this means that the axis of symmetry is also x=-2.


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


y=x%5E2%2B4x-5 Start with the given equation.


y=%28-2%29%5E2%2B4%28-2%29-5 Plug in x=-2.


y=1%284%29%2B4%28-2%29-5 Square -2 to get 4.


y=4%2B4%28-2%29-5 Multiply 1 and 4 to get 4.


y=4-8-5 Multiply 4 and -2 to get -8.


y=-9 Combine like terms.


So the y-coordinate of the vertex is y=-9.


So the vertex is .