Question 156920: Graph the quadratic equation, label the ordered pairs for the vertex and the y-intercept
y= x^2 + x-2
Found 2 solutions by Alan3354, checkley77:
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! Graph the quadratic equation, label the ordered pairs for the vertex and the y-intercept
y= x^2 + x-2
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| Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc) |
Quadratic equation  (in our case  ) has the following solutons:
For these solutions to exist, the discriminant  should not be a negative number.
First, we need to compute the discriminant :  .
Discriminant d=9 is greater than zero. That means that there are two solutions:  .
Quadratic expression  can be factored:
Again, the answer is: 1, -2.
Here's your graph:
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The vertex is at the minimum. To solve for the minimum, set the 1st derivative to 0.
2x+1 = 0
x = -1/2
Sub -1/2 for x into the eqn.
y(min) = (-1/2)^2 +(-1/2) -2
y(min) = 1/4 -1/2 - 2
= -2 1/4 = -9/4
So the vertex is (-1/2,-9/4)
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The y-intercept is easier, it's where x = 0. Sub 0 for x in the original eqn:
y = 0 + 0 -2 = -2
So the point is (0,-2)
Answer by checkley77(12844)  (Show Source):
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