The answer is (it can be curved) because it's doesn't have to cross the origin and it's a U shape so it can't look like a straight line and it doesn't have a constant rate of change. :)
Answer:
D 3m - 8
Step-by-step explanation:
If we set the equation equal to 0, we can factor it to find its roots:
x² + 4x + 4 = 0
(x + 2)(x + 2) = 0
x = -2
This graph has one root, a double root, at -2. This means that a single point, which must be the vertex of the parabola, touches the x-axis at (-2, 0)
Answer:
D 90
Step-by-step explanation:
x/4 ≥ 20
Multiply each side by 4
4*x/4 ≥ 20*4
x ≥ 80
The only number greater than or equal to 80 is 90
Let p(x) be a polynomial, and suppose that a is any real
number. Prove that
lim x→a p(x) = p(a) .
Solution. Notice that
2(−1)4 − 3(−1)3 − 4(−1)2 − (−1) − 1 = 1 .
So x − (−1) must divide 2x^4 − 3x^3 − 4x^2 − x − 2. Do polynomial
long division to get 2x^4 − 3x^3 − 4x^2 – x – 2 / (x − (−1)) = 2x^3 − 5x^2 + x –
2.
Let ε > 0. Set δ = min{ ε/40 , 1}. Let x be a real number
such that 0 < |x−(−1)| < δ. Then |x + 1| < ε/40 . Also, |x + 1| <
1, so −2 < x < 0. In particular |x| < 2. So
|2x^3 − 5x^2 + x − 2| ≤ |2x^3 | + | − 5x^2 | + |x| + | − 2|
= 2|x|^3 + 5|x|^2 + |x| + 2
< 2(2)^3 + 5(2)^2 + (2) + 2
= 40
Thus, |2x^4 − 3x^3 − 4x^2 − x − 2| = |x + 1| · |2x^3 − 5x^2
+ x − 2| < ε/40 · 40 = ε.
