SOLUTION: Find y-intercept and vertex y = x^2 - 3x - 4

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Question 91110: Find y-intercept and vertex y = x^2 - 3x - 4
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
To find the y-intercept, plug in x=0

Lets find the value of y when x=0

y=x%5E2-3x-4 Start with the given polynomial


y=%280%29%5E2-3%280%29-4 Plug in x=0


y=%280%29-3%280%29-4 Raise 0 to the second power to get 0


y=%280%29-0-4 Multiply 3 by 0 to get 0


y=-4 Remove any zero terms


So when x=0, y=-4

So the y-intercept is (0,-4)


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To determine the x-value of the vertex, use this formula
x=-b%2F%282a%29

From the equation y=x%5E2-3x-4 we can see that a=1 and b=-3

x=%28--3%29%2F%282%2A1%29 Plug in b=-3 and a=1


x=3%2F%282%2A1%29 Negate -3 to get 3


x=%283%29%2F2 Multiply 2 and 1 to get 2

x=3%2F2 Reduce



So the x-coordinate of the vertex is x=3%2F2 (which is x=1.5 in decimal form). Lets plug this into the equation to find the y-coordinate of the vertex.


Lets evaluate f%281.5%29

f%28x%29=x%5E2-3x-4 Start with the given polynomial


f%281.5%29=%281.5%29%5E2-3%281.5%29-4 Plug in x=1.5


f%281.5%29=2.25-3%281.5%29-4 Raise 1.5 to the second power to get 2.25


f%281.5%29=2.25-4.5-4 Multiply -3 and 1.5 to get -4.5


f%281.5%29=-6.25 Now combine like terms


So the vertex is (1.5,-6.25)


Here is a graph to see the vertex and y-intercept

+graph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C+x%5E2-3x-4%29+