Question

question 1
1 pts
suppose the value x = 5 is a zero of a function f(x). what does this mean?
there is a horizontal intercept at x = 5
the point (5, 0) is on the graph of f(x)
f(5)=0
all of these answer - choices describe what it means for x = 5 to be a zero of f(x)
question 2
1 pts
given h(a)=-3(a + 4)(a - 1), what are the zeros of the function?
4 and - 1
-4 and 1 and -3
4 and -1 and 3
-4 and 1
question 3
1 pts
if the zeros of a function g(x) are -7 and 3, which of the following could be a possible formula for g(x)?
g(x)=-2(x - 7)(x - 3)
g(x)=-2(x+7)(x - 3)
g(x)=7(x+3)
g(x)=-7

Explanation:

Question 1

Step1: Recall zero - function definition

A zero of a function \(y = f(x)\) is a value of \(x\) for which \(f(x)=0\). The point \((x,0)\) lies on the graph of the function, and \(x\) is an \(x\) - intercept (horizontal intercept). If \(x = 5\) is a zero of \(f(x)\), then \(f(5)=0\), the point \((5,0)\) is on the graph of \(f(x)\), and there is a horizontal intercept at \(x = 5\).

Question 2

Step1: Set the function equal to zero

Given \(h(a)=-3(a + 4)(a - 1)\), we set \(h(a)=0\). Using the zero - product property, if \(AB = 0\), then either \(A = 0\) or \(B=0\). So \(a+4 = 0\) gives \(a=-4\) and \(a - 1=0\) gives \(a = 1\). The zeros of the function are \(a=-4\) and \(a = 1\).

Question 3

Step1: Use the zero - factor form of a polynomial

If the zeros of a function \(g(x)\) are \(x=-7\) and \(x = 3\), then \((x + 7)\) and \((x - 3)\) are factors of \(g(x)\). A possible formula for \(g(x)\) is of the form \(g(x)=k(x + 7)(x - 3)\) where \(k\) is a non - zero constant. If \(k=-2\), then \(g(x)=-2(x + 7)(x - 3)\).

Answer:

Question 1: D. All of these answer choices describe what it means for \(x = 5\) to be a zero of \(f(x)\)
Question 2: D. \(-4\) and \(1\)
Question 3: B. \(g(x)=-2(x + 7)(x - 3)\)