If the graph of the polynomial $f\left(x\right)=a_0{x}^n+a_1{x}^{n-1}+a_2{x}^{n-2}+ . . . +a_n=0$ passes through the origin, then prove that $a_n=0$.

In the figure, the graph of a polynomial, $f\left(x\right)$ is given, find the zeroes of the polynomial.

In the figure, the graph of $y=f\left(x\right)$ is shown. Find the number of real zeroes of $f\left(x\right)$.

In the figure, the graph of $f\left(x\right)$ is shown.  Find the number of zeroes of $f\left(x\right)$.

In the figure, the graph of $f\left(x\right)=a{x}^2+bx+1$ is shown.  Write the signs of $a$ and $b^2-4ac$.

In the figure the graph of $f\left(x\right)=a{x}^2+bx+c$ is shown. What is the value of $b^2-4ac$ and the number of real zeroes of $f\left(x\right)$.

The graph of a quadratic polynomial $p\left(x\right)=5x^2+3x+2$ is an upward parabola.

The graph of a quadratic polynomial $q\left(x\right)=-3x^2+2$ is an upward parabola.

True/False Questions

The zeroes of  polynomial $p\left(x\right)=x^2-9x$ are equal in magnitude but opposite in sign.