Question

Which equation represents a quadratic function with a leading coefficient of 2 and a constant term of –3?

Answer 1

Quadratic equation

General form. A quadratic function $f(x)$ is of the form $(ax^{2}+bx+c)$ where $a,\:b,\:c\in\mathbb{R}$ or $\mathbb{C}$ and $a\neq 0$.

We obtain an equation when $f(x)=0$

$\Rightarrow ax^{2}+bx+c=0$ is an quadratic equation.

Solution.

Given, $a=2,\:c=-3$, but $b$ is not given.

Thus the quadratic function with leading coefficient $a=2$ and constant term $c=-3$ is given by

$\quad\quad f(x)=2x^{2}+bx-3$

$\therefore$ the required quadratic equation is

$\quad\quad 2x^{2}+bx-3=0$.

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