I encounter that quadratic inequality can have two ways of graphing, line(s) with the area of solutions and parts of a parabola. How is that happen?
1 Answer
This is similar to your previous question.
If you are looking for $x$ such that
\[x^2-4x\geq 14,\]
then
\[x^2-4x- 14\geq 0.\]
Finding the roots using the quadratic formula, you get
\[x_1,x_2=\frac{+4\pm\sqrt{14+56}}{2}=\frac{+4\pm\sqrt{70}}{2}.\]
Hence the inequality is satisfied if
\[ x\geq \frac{+4+\sqrt{70}}{2} \text{or} x\leq \frac{+4-\sqrt{70}}{2},\]
which are two line segments if graphed on $x$-axis.
However, if you view this problem as the graph of the function $y=x^2-4x- 14$, then you want the portion of the graph that lies above $x$-axis, i.e. $y=x^2-4x- 14\geq 0.$
So it is the same problem, viewed from two different points of view. The first view is one dimensional where we only have the variable $x$, while in the second case we view the problem in two dimensions and have two variables $x,y$.
Erdos
-
If you find my solutions helpful, I would appreciate a tip!
-
Thank you very much for your answer, this is so helpful. But, I’m really sorry that I can’t give you any tips since I don’t have a bank account yet. Sorry and thank you very much!
-
It's alright. I am glad I was able to help.
-
- 1 Answer
- 121 views
- Pro Bono
Related Questions
- Tensor Product II
- Three questions on Vectors
- College Algebra Help
- Compounding interest of principal P, where a compounding withdrawal amount W get withdrawn from P before each compounding of P.
- How do you prove that when you expand a binomial like $(a+b)^n$ the coefficients can be calculated by going to the n row in Pascal's triangle?
- Determine the Closed Form of a Recurrance Relation
- Prove that ${n\choose 2}2^{n-2}=\sum\limits_{k=2}^{n}{n\choose k}{k\choose 2}$ for all $n\geq 2$
- Find $a,b,c$ so that $\begin{bmatrix} 0 & 1& 0 \\ 0 & 0 & 1\\ a & b & c \end{bmatrix} $ has the characteristic polynomial $-\lambda^3+4\lambda^2+5\lambda+6=0$
Your question is very unclear. I am not sure what you are actually asking about. Please write your question more carefully. It might be a good idea to include an example to make it even more clear.
Oh thank you for telling me