Find the roots and use them to graph the related function.
{ x| - 4 ≤ x ≤ 6 }
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=x^2-2x-24 ⇔ y= 1x^2+( - 2)x+ - 24
We see that a= 1, b= - 2, and c= - 24. Let's substitute these values into the Quadratic Formula to find the roots of x^2-2x-24=0.
Now we can calculate the first root using the positive sign and the second root using the negative sign.
x=2 ± 10/2
x=2 + 10/2
x=2 - 10/2
x=2/2+10/2
x=2/2-10/2
x=6
x= - 4
The solution of the given quadratic inequality, x^2-2x-24≤0, consists of x-values for which the graph of the related quadratic function lies on and below the x-axis. The graph opens upwards since a= 1 is greater than zero.
We see that the graph lies on and below the x-axis between x=- 4 and x=6.
{ x| - 4 ≤ x ≤ 6 }
⇕
[- 4,6 ]
Showing Our Work
Drawing the parabola using roots and vertex
We already know the roots, which are around - 4 and 6. 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= - 2 into - b2a.
