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What are the [tex]$x$[/tex]-intercepts of this quadratic function?

[tex]\[ g(x) = -2(x-4)(x+1) \][/tex]

A. [tex]$(4,0)$[/tex] and [tex]$(1,0)$[/tex]
B. [tex]$(-4,0)$[/tex] and [tex]$(-1,0)$[/tex]
C. [tex]$(-4,0)$[/tex] and [tex]$(1,0)$[/tex]
D. [tex]$(4,0)$[/tex] and [tex]$(-1,0)$[/tex]



Answer :

GinnyAnswer
To determine the [tex]$x$[/tex]-intercepts of the quadratic function [tex]\( g(x) = -2(x-4)(x+1) \)[/tex], we need to find the values of [tex]\( x \)[/tex] for which [tex]\( g(x) = 0 \)[/tex].

Let's set the function equal to zero and solve for [tex]\( x \)[/tex]:

[tex]\[ g(x) = -2(x-4)(x+1) = 0 \][/tex]

The product of two factors is zero if at least one of the factors is zero. Therefore, we need to solve the equations:

[tex]\[ (x-4) = 0 \][/tex]
and
[tex]\[ (x+1) = 0 \][/tex]

Solving these equations for [tex]\( x \)[/tex]:

1. For [tex]\( (x-4) = 0 \)[/tex]:
[tex]\[ x = 4 \][/tex]

2. For [tex]\( (x+1) = 0 \)[/tex]:
[tex]\[ x = -1 \][/tex]

Thus, the [tex]\( x \)[/tex]-intercepts of the function [tex]\( g(x) = -2(x-4)(x+1) \)[/tex] are [tex]\( (4, 0) \)[/tex] and [tex]\( (-1, 0) \)[/tex].

So, the correct answer is:

D. [tex]\((4,0)\)[/tex] and [tex]\((-1,0)\)[/tex]

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