Determine the x-intercepts of the following equation. (-x-1)(x-3)=y (3,0) (-1,0) and (3,0) (0,3) (0,-3) (0,-1) and (0,3) (-1,0) and (-3,0)

Set y to 0: To find the x-intercepts of the equation, we need to set y to 0 and solve for x. This is because the x-intercepts are the points where the graph of the equation crosses the x-axis, and at these points, the y-coordinate is 0. (-x-1)(x-3) = 0Apply zero product property: Now we have a product of two factors equal to zero. According to the zero product property, if the product of two factors is zero, then at least one of the factors must be zero. Therefore, we can set each factor equal to zero and solve for x. First factor: -x - 1 = 0 Second factor: x - 3 = 0Solve first factor: Solve the first factor for x: -x - 1 = 0 -x = 1 x = -1Solve second factor: Solve the second factor for x: x - 3 = 0 x = 3Identify x-intercepts: We have found two values of x for which y equals zero. These are the x-intercepts of the equation. The x-intercepts are (-1, 0) and (3, 0).

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Determine the
x-intercepts of the following equation.

(-x-1)(x-3)=y

(3,0)

(-1,0) and
(3,0)

(0,3)

(0,-3)

(0,-1) and
(0,3)

(-1,0) and
(-3,0)

Determine the $x$ -intercepts of the following equation. $\newline$ $(-x-1)(x-3)=y$ $\newline$ $(3,0)$ $\newline$ $(-1,0)$ and $(3,0)$ $\newline$ $(0,3)$ $\newline$ $(0,-3)$ $\newline$ $(0,-1)$ and $(0,3)$ $\newline$ $(-1,0)$ and $(-3,0)$

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Math Problems

Algebra 2

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

Full solution

Q. Determine the

x

-intercepts of the following equation.

\newline

(-x-1)(x-3)=y

\newline

(3,0)

\newline

(-1,0)

and

(3,0)

\newline

(0,3)

\newline

(0,-3)

\newline

(0,-1)

and

(0,3)

\newline

(-1,0)

and

(-3,0)

Set $y$ to $0$ : To find the $x$ -intercepts of the equation, we need to set $y$ to $0$ and solve for $x$ . This is because the $x$ -intercepts are the points where the graph of the equation crosses the $x$ -axis, and at these points, the $y$ -coordinate is $0$ . $(-x-1)(x-3) = 0$
Apply zero product property: Now we have a product of two factors equal to zero. According to the zero product property, if the product of two factors is zero, then at least one of the factors must be zero. Therefore, we can set each factor equal to zero and solve for $x$ . $\newline$ First factor: $-x - 1 = 0$ $\newline$ Second factor: $x - 3 = 0$
Solve first factor: Solve the first factor for $x$ : $-x - 1 = 0$ $-x = 1$ $x = -1$
Solve second factor: Solve the second factor for $x$ : $x - 3 = 0$ $x = 3$
Identify x-intercepts: We have found two values of $x$ for which $y$ equals zero. These are the x-intercepts of the equation. The x-intercepts are $(-1, 0)$ and $(3, 0)$ .