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Which point is an [tex]\(x\)[/tex]-intercept of the quadratic function [tex]\(f(x) = (x+6)(x-3)\)[/tex]?

A. [tex]\((0,6)\)[/tex]
B. [tex]\((0,-6)\)[/tex]
C. [tex]\((6,0)\)[/tex]
D. [tex]\((-6,0)\)[/tex]



Answer :

GinnyAnswer
To determine which point is an [tex]$x$[/tex]-intercept of the quadratic function [tex]\( f(x) = (x+6)(x-3) \)[/tex], we need to understand the definition of [tex]$x$[/tex]-intercepts. An [tex]$x$[/tex]-intercept is where the graph of the function crosses the x-axis, which occurs when [tex]\( f(x) = 0 \)[/tex].

Given the function [tex]\( f(x) = (x+6)(x-3) \)[/tex], we set [tex]\( f(x) \)[/tex] to 0 and solve for [tex]\( x \)[/tex]:

[tex]\[ (x + 6)(x - 3) = 0 \][/tex]

This equation will be true when any of its factors is equal to zero.

1. Solve for [tex]\( x + 6 = 0 \)[/tex]:
[tex]\[ x + 6 = 0 \][/tex]
[tex]\[ x = -6 \][/tex]

2. Solve for [tex]\( x - 3 = 0 \)[/tex]:
[tex]\[ x - 3 = 0 \][/tex]
[tex]\[ x = 3 \][/tex]

Therefore, the [tex]$x$[/tex]-intercepts of the function [tex]\( f(x) = (x+6)(x-3) \)[/tex] are at [tex]\( x = -6 \)[/tex] and [tex]\( x = 3 \)[/tex].

So, the points where the function crosses the x-axis are [tex]\( (-6, 0) \)[/tex] and [tex]\( (3, 0) \)[/tex].

Looking at the given choices, the correct answer for which point is an [tex]$x$[/tex]-intercept of the quadratic function [tex]\( f(x) = (x+6)(x-3) \)[/tex] is:

[tex]\[ \boxed{(-6,0)} \][/tex]

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