SOLUTION: Y=x^2-2x-1 Y=-3x+5

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Question 198500: Y=x^2-2x-1
Y=-3x+5
Answer by jojo14344(1513) About Me  (Show Source):
You can put this solution on YOUR website!


Given:system%28Y=x%5E2-2x-1%28red%28EQN1%29%29%2CY=-3x%2B5%28red%28EQN2%29%29%29


In red%28EQN1%29, it's a parabola and follows the form Ax%5E2%2BBx%2BC=0

For the Vertex, x=-b%2F2a=-%28-2%29%2F%282%2A1%29=2%2F2=red%281%29,
Substitute to the Eqn to Y:
Y=1%5E2-2%281%29-1=1-2-1=red%28-2%29

The Vertex ----> (1,-2)

We solve the eqn to find the x-Intercepts:
x%5E2-2x-1=0

For the Discriminant: b%5E2-4ac=-2%5E2-4%281%29%28-1%29=4%2B4=8

Then,
x=%28-%28-2%29%2B-sqrt%288%29%29%2F%282%2A1%29=%282%2B-2.83%29%2F2
x=%282%2B2.83%29%2F2=4.83%2F2=red%282.415%29
x=%282-2.83%29%2F2=-.83%2F2=red%28-0.415%29

We see the graph,
--->


In red%28EQN2%29, is a Line with the form Ax%2BBy%2BC=0.

Y=-3x%2B5
Let Fy=0
0=-3x%2B5 ---> 3x=5 ----> cross%283%29x%2Fcross%283%29=5%2F3
red%28x=5%2F3%29, x-Intercept (5/3,0) = (1.67,0)

Let Fx=0
y=-3%280%29%2B5
red%28y=5%29, y-Intercept (0,5)

--->

Thank you,
Jojo