Respuesta :
The x-intercept of a quadratic function is the x-value of the function (if there is any) that has a y-coordinate of zero. Hence, you can solve for the roots of this function and if you're using a graphing calculator, you may graph this function to find the roots that intercepts the x-axis. You could also just substitute 0 for f(x), since f(x)=y and that'd be the equivalent of having a y-coordinate of zero to find the x-intercept.
Answer:
[tex](-6,0)[/tex]
[tex](3,0)[/tex]
Step-by-step explanation:
We have been given an quadratic function [tex]f(x)=(x+6)(x-3)[/tex].
To find the x-intercept of he given function, we will equate our given function equal to zero.
Using zero product property we will get,
[tex](x+6)(x-3)=0[/tex]
[tex](x+6)=0\text{ or }(x-3)=0[/tex]
[tex]x+6=0\text{ (or) }x-3=0[/tex]
[tex]x+6-6=0-6\text{ (or) }x-3+3=0+3[/tex]
[tex]x=-6\text{ (or) }x=3[/tex]
Since y-coordinate is zero at x-axis, therefore, the x-intercepts of our given function would be [tex](-6,0)[/tex] and [tex](3,0)[/tex].
