Q4. - Algebra 1

Question

Use a table of values to graph the given equation. State the domain and range.

$y=-3x^2-x+1$

Step-by-Step Solution

Answer

The graph of the given function is

 

The domain is $\left(-\infty ,\infty \right)$ and the range is $[-\frac{13}{12}\mathbf{,}\infty )$.

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 domain and range of a function.

The domain is the set of all of the possible values of the independent variable $x$.

The range is the set of all the possible values of the dependent variable $y$.

Step 3. Calculate the table of values for the function y = − 3 x 2 − x + 1 .

$x$	$y$
$-2$	$-1$
$-1$	$-1$
0	$-3$
1	$-7$
2	$-13$

Step 4. Use the table of values to graph the function y = − 3 x 2 − x + 1 .

Graph the ordered pairs from the table and connect them to create a smooth curve.

Step 5. State the domain and range for function y = − 3 x 2 − x + 1 .

Observe the graph.

The parabola extends to infinity. 

So, the domain is $\left(-\infty ,\infty \right)$.

The minimum value of the function is $-\frac{13}{12}$.

So, the range is $\left[-\frac{13}{12}\right.,\left.\infty \right)$.

Therefore, the domain is $\left(-\infty ,\infty \right)$ and the range is  $\left[-\frac{13}{12}\right.,\left.\infty \right)$.