Determine the x-intercepts of the following equation. (-x-1)(x+5)=y (0,-5) (0,5) (-5,0) (-1,0) and (-5,0) (-1,0) and (5,0) (0,-1) and (0,-5)

Concept of x-intercepts: Understand the concept of x-intercepts. The x-intercepts of an equation are the points where the graph of the equation crosses the x-axis. At these points, the value of y is 0.Set equation to zero: Set the equation equal to zero to find the x-intercepts. (-x-1)(x+5)=y To find the x-intercepts, we set y to 0: (-x-1)(x+5)=0Solve for x: Solve the equation for x to find the x-intercepts. We have a product of two factors equal to zero, so we can use the zero product property, which states that if a product of factors is zero, then at least one of the factors must be zero. So, we set each factor equal to zero and solve for x: -x-1=0 or x+5=0First factor solution: Solve the first factor for x. -x-1=0 Add 1 to both sides: -x=1 Multiply both sides by -1: x=-1Second factor solution: Solve the second factor for x. x+5=0 Subtract 5 from both sides: x=-5Write x-intercepts: Write down the x-intercepts. The x-intercepts are the x-values we found by solving the equation. They are (-1,0) and (-5,0).

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Determine the
x-intercepts of the following equation.

(-x-1)(x+5)=y

(0,-5)

(0,5)

(-5,0)

(-1,0) and
(-5,0)

(-1,0) and
(5,0)

(0,-1) and
(0,-5)

Determine the $x$ -intercepts of the following equation. $\newline$ $(-x-1)(x+5)=y$ $\newline$ $(0,-5)$ $\newline$ $(0,5)$ $\newline$ $(-5,0)$ $\newline$ $(-1,0)$ and $(-5,0)$ $\newline$ $(-1,0)$ and $(5,0)$ $\newline$ $(0,-1)$ and $(0,-5)$

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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+5)=y

\newline

(0,-5)

\newline

(0,5)

\newline

(-5,0)

\newline

(-1,0)

and

(-5,0)

\newline

(-1,0)

and

(5,0)

\newline

(0,-1)

and

(0,-5)

Concept of $x$ -intercepts: Understand the concept of $x$ -intercepts. The $x$ -intercepts of an equation are the points where the graph of the equation crosses the $x$ -axis. At these points, the value of $y$ is $0$ .
Set equation to zero: Set the equation equal to zero to find the $x$ -intercepts. $(-x-1)(x+5)=y$ To find the $x$ -intercepts, we set $y$ to $0$ : $(-x-1)(x+5)=0$
Solve for x: Solve the equation for x to find the x-intercepts. $\newline$ We have a product of two factors equal to zero, so we can use the zero product property, which states that if a product of factors is zero, then at least one of the factors must be zero. $\newline$ So, we set each factor equal to zero and solve for x: $\newline$ $-x-1=0$ or $x+5=0$
First factor solution: Solve the first factor for $x$ . $-x-1=0$ Add $1$ to both sides: $-x=1$ Multiply both sides by $-1$ : $x=-1$
Second factor solution: Solve the second factor for $x$ . $x+5=0$ Subtract $5$ from both sides: $x=-5$
Write x-intercepts: Write down the x-intercepts. $\newline$ The x-intercepts are the x-values we found by solving the equation. They are $(-1,0)$ and $(-5,0)$ .