Join IDNLearn.com today and start getting the answers you've been searching for. Receive prompt and accurate responses to your questions from our community of knowledgeable professionals ready to assist you at any time.
Sagot :
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 points where the function crosses the [tex]\(x\)[/tex]-axis. This occurs when [tex]\(g(x) = 0\)[/tex].
Setting the function equal to zero, we have:
[tex]\[ -2(x-4)(x+1) = 0 \][/tex]
Next, we solve for the values of [tex]\(x\)[/tex] that make this equation true. We can use the Zero Product Property, which states that if a product of factors equals zero, then at least one of the factors must be zero.
We have two factors in our equation: [tex]\((x-4)\)[/tex] and [tex]\((x+1)\)[/tex]. We set each factor equal to zero and solve for [tex]\(x\)[/tex].
1. Set [tex]\(x-4=0\)[/tex]:
[tex]\[ x - 4 = 0 \implies x = 4 \][/tex]
2. Set [tex]\(x+1=0\)[/tex]:
[tex]\[ x + 1 = 0 \implies x = -1 \][/tex]
Thus, the [tex]\(x\)[/tex]-intercepts of the function are the points [tex]\((4, 0)\)[/tex] and [tex]\((-1, 0)\)[/tex].
Therefore, the correct answer is:
C. [tex]\((4,0)\)[/tex] and [tex]\((-1,0)\)[/tex]
Setting the function equal to zero, we have:
[tex]\[ -2(x-4)(x+1) = 0 \][/tex]
Next, we solve for the values of [tex]\(x\)[/tex] that make this equation true. We can use the Zero Product Property, which states that if a product of factors equals zero, then at least one of the factors must be zero.
We have two factors in our equation: [tex]\((x-4)\)[/tex] and [tex]\((x+1)\)[/tex]. We set each factor equal to zero and solve for [tex]\(x\)[/tex].
1. Set [tex]\(x-4=0\)[/tex]:
[tex]\[ x - 4 = 0 \implies x = 4 \][/tex]
2. Set [tex]\(x+1=0\)[/tex]:
[tex]\[ x + 1 = 0 \implies x = -1 \][/tex]
Thus, the [tex]\(x\)[/tex]-intercepts of the function are the points [tex]\((4, 0)\)[/tex] and [tex]\((-1, 0)\)[/tex].
Therefore, the correct answer is:
C. [tex]\((4,0)\)[/tex] and [tex]\((-1,0)\)[/tex]
Your participation is crucial to us. Keep sharing your knowledge and experiences. Let's create a learning environment that is both enjoyable and beneficial. For trustworthy answers, rely on IDNLearn.com. Thanks for visiting, and we look forward to assisting you again.