Question

The graph of a quadratic polynomial is ____?

Answer 1

Parabloa:

The standard form of a quadratic polynomial is$\mathrm{f}\left(\mathrm{x}\right)={\mathrm{ax}}^2+\mathrm{bx}+\mathrm{c}$

Which is a curve with the equation

$\mathrm{f}\left(\mathrm{x}\right)={\mathrm{ax}}^2+\mathrm{bx}+\mathrm{c}$

We must first find the vertex for the given equation before drawing a parabola graph.

$x=\frac{-\mathrm{b}}{2\mathrm{a}}$ and$\mathrm{y}=\mathrm{f}\left(\frac{-\mathrm{b}}{2\mathrm{a}}\right)$ can be used to accomplish this.

Plotting the graph, when the quadratic equation is given in the form of $\mathrm{f}\left(\mathrm{x}\right)=\mathrm{a}{(\mathrm{x}-\mathrm{h})}^2+\mathrm{k}$ where $(\mathrm{h},\mathrm{k})$ is the vertex of the parabola, is its vertex form.

The graph of$\mathrm{f}\left(\mathrm{x}\right)={\mathrm{ax}}^2+\mathrm{bx}+\mathrm{c}$,$\mathrm{a}\ne 0$, is a parabola that opens upward if $\mathrm{a}>0$ and downward if $\mathrm{a}<0$.

Hence, the graph of a quadratic polynomial is a parabola.