Find the value of so that the graph of the following system of
equations has no solution.
3 − 2 − 12 = 0
+ 6 − 10 = 0
Offer a geometric explanation to why the equation
2 − 6 + 10 = 0
has no real solutions.
Without his pencil or calculator, Joey knows that 2
3 + 3
2 − 1 = 0
has at least one real solution. How does he know?
The graph of the quadratic equation =
2 + 1 has no -intercepts.
However, Gia claims that when the graph of =
2 + 1 is translated
by a distance of 1 in a certain direction, the new (translated) graph
would have exactly one -intercept. Further, if =
2 + 1 is
translated by a distance greater than 1 in the same direction, the new
(translated) graph would have exactly two -intercepts. Support or
refute Gia’s claim. If you agree with her, in which direction did she
translate the original graph? Draw graphs to illustrate