Formation of Quadratic Equation

Let the graph of $g$ be a translation $3$ units right and $2$ units up, followed by a reflection in the $y-$axis of the graph of $f\left(x\right)=x^2-5x$. Write a rule for $g$.

Describe the transformation of $f\left(x\right)=x^2$ represented by $g$. Then graph each function.

$g\left(x\right)=4x^2+1$

Describe the transformation of $f\left(x\right)=x^2$ represented by $g\left(x\right)={(x-3)}^2+5$ .

Describe the transformation of $f\left(x\right)=x^2$ represented by $g\left(x\right)={(x + 4)}^2-1$ . Then graph each function.

If $\alpha ,\beta$ are the roots of the quadratic equation $a{x}^2+bx+c=0$, then ${\left(\log \left(\frac{1}{\alpha }\right)\right)}^2+{\left(\log \left(\frac{1}{\beta }\right)\right)}^2$  will be the symmetric function of roots.

If $A,B$ are the roots of the quadratic equation $a{x}^2+bx+c=0$, then $\tan (A-B)$  will be the symmetric function of roots.

If $\alpha ,\beta$ are the roots of the quadratic equation $a{x}^2+bx+c=0$, then $\left|\log \left(\frac{\alpha }{\beta }\right)\right|$  will be the symmetric function of roots.

If $\alpha ,\beta$ are the roots of the quadratic equation $a{x}^2+bx+c=0$, then ${\alpha }^2{\beta }^5+{\beta }^2{\alpha }^5$  will be the symmetric function of roots.

If $\alpha ,\beta$ are roots of the quadratic equation $a{x}^2+bx+c=0$, form an equation whose roots are $\alpha +\beta ,\alpha \beta$.

If $\alpha +\beta =5$ and ${\alpha }^3+{\beta }^3=35$, then the quadratic equation whose roots are $\alpha$ and $\beta$ is

If $\alpha , \beta$ are the zeroes of a polynomial $x^2-ax+b$ , such that $\alpha +\beta =6$ and $\alpha \beta =4$, then find the value of $\left(a+b\right)$.

Cotyledons are also called-

If $5p^2-7p-3=0$ and $5q^2-7q-3=0, p\ne q$ , then the equation whose roots are $5p-4q$ and $5q-4p$ is

Let $\alpha , \beta$ be the roots of $x^2+3x+5=0$$,$ then the equation whose roots are $-\frac{1}{\alpha }$ and $-\frac{1}{\beta }$ is

If $\mathrm{\alpha },\mathrm{ }\mathrm{\beta }$ are the roots of the quadratic equation $\mathrm{a}{\mathrm{x}}^2+\mathrm{b}\mathrm{x}+\mathrm{c}=0$ then the quadratic equation whose roots are ${\mathrm{\alpha }}^3,\mathrm{ }{\mathrm{\beta }}^3$ is

If $\mathrm{\alpha },\mathrm{ }\mathrm{\beta }$ are the roots of $a{x}^2+bx+c=0$ then the quadratic equation whose roots are $2\mathrm{\alpha }+3\mathrm{ }$ and $2\mathrm{\beta }+3$ is

If m and n are two numbers such that $\mathrm{m}\mathrm{ }+\mathrm{ }\mathrm{n}\mathrm{ }=\mathrm{ }3$ and $\mathrm{m}\mathrm{ }-\mathrm{ }\mathrm{n}\mathrm{ }=\mathrm{ }19$ , then what is the quadratic polynomial whose zeroes are m and n?

The quadratic equation whose roots are the $\mathrm{x}$ and $\mathrm{y}$ intercepts of the line passing through $\left(1,\mathrm{ }1\right)$ and making a triangle of area $\mathrm{A}$ with the axes may be-

The equation whose roots are reciprocal of the roots of the equation $3{\mathrm{x}}^2-\mathrm{ }20\mathrm{x}+17=0$ is -

The value of $a$ for which the sum of the squares of the roots of the equation $x^2-\left(a-2\right)x-a-1=0$  assume the least value is