Quadratic Function Real Life Examples and Applications

Why do I get incorrect solutions ${\displaystyle x=0}$ and ${\displaystyle x=2}$ for ${\displaystyle x+1+\sqrt{4x+1}=0?}$

Solving quadratic matrix equation for X
$X^2=\left[\begin{array}{cc}1& a\\ 0& 1\end{array}\right]$
where ${\displaystyle a\in \frac{\mathbb{R}}{0}}$. Solve for matrix X.

Find real solution to the equation
${\displaystyle 3x^2+3y^2-4xy+10x-10y+10=0.}$
What does partial differentiation give for a second degree equation which doesn't represent a conic?

Factoring ${\displaystyle 2k^2+7k+6}$

Does every quadratic polynomial defined in real numbers always define a function?
For example, let a,b,c ${\displaystyle \in \mathbb{R}}$ and define
${\displaystyle P\left(x\right)=a{x}^2+bx+c}$

Solve fractional inequalities that have quadratics
${\displaystyle \frac{2x^2+3x-2}{2x^2-3x-2}>0}$
How do you find the range of solutions? Can you just bring the denominator onto the right hand side or does that lose solutions?

Find all values of a and b that will make
${\displaystyle (ax+5)2=16x2+bx+25}$ true for all x.

Integer between the 's p and ${\displaystyle p+2}$ is a perfect square. Explain why there exists an integer n such that
${\displaystyle 4n^2-1=p}$
a) Is the integer between p and ${\displaystyle p+2}$ odd or even?
b) Assume additionally that the integer between the 's p and ${\displaystyle p+2}$ is a perfect square.
c) By considering ${\displaystyle (2n-1)(2n+1)}$, find the only possible value of p.

Are there any two real nonzero numbers a and b such that ${\displaystyle a^2+ab+b^2=0}$ Why or why not?

This scenrio has do around QUADRATICS problems.
You have been asked to bake the birthday cake of a little girl who is about to turn three. When looking up suggestions online on how to bake this cake, you found that most everyone suggests baking the cake in smaller circular cake pans that have a diameter of 6 inches. That’s the best way to get the height for the unicorn head. A normal circular cake pan (and the only kind you have) has a diameter of 9 inches. You need to buy cake pans. As an experienced baker, you know that the recipe you are planning on using usually fills two regular (9-inch) cake pans, with a little room to spare. How many 6-inch pans do you need to buy? (We’re going to assume that all cake pans are the same height.)

The complex zeros of f 1x2 = x4 + 1 For the function f1x2 = x4 + 1:
(a) Factor f into the product of two irreducible quadratics. (Hint: Complete the square by adding and
subtracting 2x2
.2
(b) Find the zeros of f by finding the zeros of each irreducible quadratic.

How do you know if ${\displaystyle y=16-4x^2}$ pens up or down?

What is the axis of symmetry of the graph of
${\displaystyle y=2{(x-3)}^2+5}$?

What is the axis of symmetry of the graph of ${\displaystyle y=-x^2-2x-1}$?

What is the axis of symmetry of the graph of ${\displaystyle y=7(x+1)(x-3)?}$

How do you graph the quadratic function
${\displaystyle y=-x^2+2x+4}$

How do you graph the quadratic equation after completing the given table of values ${\displaystyle y=x^2-2x?}$

How do you graph ${\displaystyle y=-x^2-4x-3?}$

What are the x-intercepts of ${\displaystyle y=x^2+2x-15?}$

How do you find the vertex of ${\displaystyle y=2x^2+10x+8}$?