SOLUTION: What is the vertex of the graph of this function: y=(x+3)(x-5)

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Question 164513: What is the vertex of the graph of this function:
y=(x+3)(x-5)
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
y=%28x%2B3%29%28x-5%29 Start with the given equation


y=x%5E2-5x%2B3x-15 FOIL


y=x%5E2-2x-15 Combine like terms.


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%5E2-2x-15, we can see that a=1, b=-2, and c=-15.


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


x=%282%29%2F%282%281%29%29 Negate -2 to get 2.


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


x=1 Divide.


So the x-coordinate of the vertex is x=1. Note: this means that the axis of symmetry is also x=1.


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


y=x%5E2-2x-15 Start with the given equation.


y=%281%29%5E2-2%281%29-15 Plug in x=1.


y=1%281%29-2%281%29-15 Square 1 to get 1.


y=1-2%281%29-15 Multiply 1 and 1 to get 1.


y=1-2-15 Multiply -2 and 1 to get -2.


y=-16 Combine like terms.


So the y-coordinate of the vertex is y=-16.


So the vertex is .