Find the roots and use them to graph the related function.
{all real numbers}
Practice makes perfect
We will start by sketching the related quadratic function. To do so, we first need to identify the values of a, b, and c.
y= 1x^2 + 8x + 16
We see that a= 1, b= 8, and c= 16. Let's substitute these values into the Quadratic Formula to find the roots of x^2+8x+16=0.
We see that there is only one root, x=- 4.
The solution of the given quadratic inequality, x^2+8x+16≥0, consists of x-values for which the graph of the related quadratic function lies on and above the x-axis. The graph opens upward since a= 1 is greater than zero.
We see that the graph lies on and above the x-axis for all x-values.
{all real numbers}
⇕
(- ∞, + ∞ )
Showing Our Work
Drawing the parabola using roots and vertex
We already know the root, which is - 4. To draw the graph, we will find the vertex, (- b2a,f(- b2a)). Let's start by calculating its x-coordinate. To do so, we will substitute a= 1 and b= 8 into - b2a.
