91Ó°ÊÓ

A quadratic function, which is written in the form, $y=a{x}^2+bx+c$, where,$a≠0$ is called the standard form of the quadratic function.

The graph of the function$y=a{x}^2+bx+c$

Opens upward and has a minimum value at $x=−\frac{b}{2a}$, when $a>0$.

Opens downward and has a maximum value at $x=−\frac{b}{2a}$, when $a<0$.

The $y$-intercept of the function$y=a{x}^2+bx+c$ is always at $y=c$.

Compare the quadratic function$y=−2x^2−4x−3$ with the standard quadratic function $y=a{x}^2+bx+c$.

$a=−2,\text{ }b=−4,\text{ }c=−3$

Substitute$a=−2$ and$b=−4$ in $x=−\frac{b}{2a}$.

$$\begin{gathered} x=−\left(\frac{−4}{2\left(−2\right)}\right) \\ x=−\left(\frac{−4}{−4}\right) \\ x=−1 \end{gathered}$$

Since, $a<0$.

So, the graph opens downward and has a maximum value at $x=−1$.

The $y$-intercept is width="51" height="20" role="math">y=−3.

The graph of the function$y=−2x^2−4x−3$ is shown below.