A cubic function is graphed in the $x y$ -plane. Which of the foll equations could represent the graph? $\newline$ Choose $1$ answer: $\newline$ (A) $y=x(x-1)(x+2)$ $\newline$ (B) $y=x(x+1)(x-2)$ $\newline$ (C) $y=-x(x-1)(x+2)$ $\newline$ (D) $y=-x(x+1)(x-2)$

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Algebra 2

Write a quadratic function from its x-intercepts and another point

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Q. A cubic function is graphed in the

x y

-plane. Which of the foll equations could represent the graph?

\newline

Choose

1

answer:

\newline

(A)

y=x(x-1)(x+2)

\newline

(B)

y=x(x+1)(x-2)

\newline

(C)

y=-x(x-1)(x+2)

\newline

(D)

y=-x(x+1)(x-2)

Determine End Behavior: Look at the sign of the leading coefficient to determine the end behavior of the cubic function. If the leading coefficient is positive, the ends of the cubic function will go off to positive infinity on both sides. If the leading coefficient is negative, the ends of the cubic function will go off to negative infinity on both sides.
Check Leading Coefficients: Check the options given: $\newline$ (A) $y=x(x-1)(x+2)$ - Positive leading coefficient. $\newline$ (B) $y=x(x+1)(x-2)$ - Positive leading coefficient. $\newline$ (C) $y=-x(x-1)(x+2)$ - Negative leading coefficient. $\newline$ (D) $y=-x(x+1)(x-2)$ - Negative leading coefficient.
Evaluate $X$ -Intercepts: Without the graph, we can't determine the end behavior directly, so we can't eliminate any options based on the leading coefficient alone.
Inconclusive Without Graph: Look at the x-intercepts given by the factors in each equation. $\newline$ (A) has x-intercepts at $x=0$ , $x=1$ , and $x=-2$ . $\newline$ (B) has x-intercepts at $x=0$ , $x=-1$ , and $x=2$ . $\newline$ (C) has x-intercepts at $x=0$ , $x=1$ , and $x=-2$ . $\newline$ (D) has x-intercepts at $x=0$ , $x=-1$ , and $x=2$ .
Inconclusive Without Graph: Look at the x-intercepts given by the factors in each equation. $\newline$ (A) has x-intercepts at $x=0$ , $x=1$ , and $x=-2$ . $\newline$ (B) has x-intercepts at $x=0$ , $x=-1$ , and $x=2$ . $\newline$ (C) has x-intercepts at $x=0$ , $x=1$ , and $x=-2$ . $\newline$ (D) has x-intercepts at $x=0$ , $x=-1$ , and $x=2$ .Without the graph, we can't determine the exact x-intercepts, so we can't choose the correct equation based on x-intercepts alone.
Inconclusive Without Graph: Look at the x-intercepts given by the factors in each equation. $\newline$ (A) has x-intercepts at $x=0$ , $x=1$ , and $x=-2$ . $\newline$ (B) has x-intercepts at $x=0$ , $x=-1$ , and $x=2$ . $\newline$ (C) has x-intercepts at $x=0$ , $x=1$ , and $x=-2$ . $\newline$ (D) has x-intercepts at $x=0$ , $x=-1$ , and $x=2$ .Without the graph, we can't determine the exact x-intercepts, so we can't choose the correct equation based on x-intercepts alone.Since we don't have enough information about the graph's end behavior or x-intercepts, we can't determine which equation is correct.