Question

Graph the function.

$y=-3x^2+6x-4$

Short answer

The graph of the function$y=-3x^2+6x-4$ is

Step-by-step solution

Step 1. Define the standard form of the quadratic function.

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

Step 2. Define the maximum or minimum point of the function y=ax2+bx+c.

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 $a<0$.

Step 3. y-intercept of the function y=ax2+bx+c.

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

Step 4. Plot the graph of the function y=−3x2+6x−4.

Compare the quadratic function $y=-3x^2+6x-4$with the standard quadratic function $y=a{x}^2+bx+c$.

$a=-3,b=6,c=-4$

Substitute$a=-3$ and$b=6$ in $x=-\frac{b}{2a}$.

$$\begin{gathered} x=-\left(\frac{6}{2\left(-3\right)}\right) \\ x=-\left(\frac{6}{-6}\right) \\ x=1 \end{gathered}$$

Since, $a<0$.

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

The $y$-intercept is $y=c$.

The graph of the function $y=-3x^2+6x-4$is shown below.