Find the roots and use them to graph the related function.
{ x| - 5 < x < - 3 }
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 + 15
We see that a= 1, b= 8, and c= 15. Let's substitute these values into the Quadratic Formula to find the roots of x^2+8x+15=0.
Now we can calculate the first root using the positive sign and the second root using the negative sign.
x=- 8 ± 2/2
x=- 8 + 2/2
x=- 8 - 2/2
x=- 8/2+2/2
x=- 10/2-2/2
x= - 3
x=- 5
The solution of the given quadratic inequality, x^2+8x+15 < 0, consists of x-values for which the graph of the related quadratic function lies below the x-axis. The graph opens upwards since a= 1 is greater than zero.
We see that the graph lies below the x-axis between x=- 5 and x=- 3.
{ x| - 5 < x < - 3 }
⇕
(- 5, - 3 )
Showing Our Work
Drawing the parabola using roots and vertex
We already know the roots, which are - 5 and - 3. 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.
