apply the quadratic formula to find the roots of the given function, and then graph the function.
f(x) = x2 - 4
g(x) = x2 - x - 12
http://www.purplemath.com/modules/quadform.htm
To find the roots of a quadratic equation, we can apply the quadratic formula, which is given by:
x = (-b ± √(b^2 - 4ac)) / (2a)
Let's apply this formula to find the roots of the given functions and then graph them.
1. For f(x) = x^2 - 4:
a = 1, b = 0, c = -4
Plug in these values into the quadratic formula:
x = (-(0) ± √((0)^2 - 4 * 1 * (-4))) / (2 * 1)
x = ± √16 / 2
x = ± 4/2
x = ± 2
Therefore, the roots of f(x) are x = 2 and x = -2.
To graph the function, we start by plotting these roots on a coordinate plane:
-2 | * | 2
|____________|
0
Next, we can find the vertex of the parabola. The vertex occurs at the x-coordinate of -b/(2a). In this case, it is -0/(2*1) = 0. So the vertex is at (0, -4).
Using this information, we can sketch the graph of the function f(x) = x^2 - 4, which is a parabola that opens upwards and intersects the x-axis at x = -2 and x = 2.