Identify the transformation that maps the figure onto itself.
1 answer:
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Given that:
y < x² + 2
y > x² - 6
Using the graphing technology:
The vertex of first equation will be: (0,2)
As, y is less than the quadratic equation, the outer portion of the parabola will be shaded and the parabola's boundary will be dotted line.
Similarly,
the second equation will vertex, (0,-6), will be a dotted parabola and the inner part of the parabola will be shaded.
Solution to the set of equations will be the common shaded region as shown in the graph attached. There is no common point which intersects both the equations.
Answer:
see explanation
Step-by-step explanation:
Given a quadratic equation in standard form
ax² + bx + c = 0 ( a ≠ 0 )
Then for the equation to have 2 real roots , the discriminant must be greater than zero , that is
b² - 4ac > 0
x² + x + c = 0 ← is in standard form
with a = 1, b = 1, c = c , then
b² - 4ac > 0
1² - (4 × 1 × c) > 0
1 - 4c > 0 ( subtract 1 from both sides )
- 4c > - 1
Divide both sides by - 4, reversing the inequality as a result of dividing by a negative quantity.
c <