Answer:
(–3, 0) and (1,0)
Step-by-step explanation:
Determining the roots (x-axis intercepts) of an equation is one of the oldest problems in mathematics and a great number of efforts have been made in this regard. Its importance is that if we can determine the roots of an equation we can also determine maxima and minima, eigenvalues of matrices, solve systems of linear and differential equations, among others.
Determining the roots of an equation can be a very difficult problem. If f (x) is a function of degree 3rd or 4th it is necessary to use complex and laborious methods. On the other hand, if f (x) is a polynomial function of degree 1st or 2nd, it is possible to use simple equations that allow us to determine its roots.
For example that graph represents a parabola which is a 2nd degree function whose general form is:
[tex]f(x)=ax^2+bx+c[/tex]
If we hadn't the graph, we could calculate the roots, using the quadratic formula:
[tex]f(x)=0\\\\x=\frac{-b \pm\sqrt{b^2-4ac} }{2a}[/tex]
But, in this case, we can extract the roots (x-intercepts ) directly from the graph. As you can see the function crosses the x-axis at the points (-3,0) and (1,0). That's it, those are the x-intercepts of the graphed function.
