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

Set y to 0: To find the x-intercepts of the equation, we need to set y to 0 and solve for x. (x-5)(x+1) = 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, at least one of the factors must be zero. So, we set each factor equal to zero and solve for x. x - 5 = 0 or x + 1 = 0Solve for x: Solving the first equation for x gives us the first x-intercept: x - 5 = 0 x = 5First x-intercept: Solving the second equation for x gives us the second x-intercept: x + 1 = 0 x = -1Second x-intercept: We have found two x-intercepts: (5, 0) and (-1, 0). These are the points where the parabola crosses the x-axis.

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Determine the
x-intercepts of the following equation.

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

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

(0,-5)

(5,0) and
(1,0)

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

(0,5)

(-5,0)

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

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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-5)(x+1)=y

\newline

(5,0)

and

(-1,0)

\newline

(0,-5)

\newline

(5,0)

and

(1,0)

\newline

(0,5)

and

(0,-1)

\newline

(0,5)

\newline

(-5,0)

Set $y$ to $0$ : To find the $x$ -intercepts of the equation, we need to set $y$ to $0$ and solve for $x$ . $(x-5)(x+1) = 0$
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, at least one of the factors must be zero. $\newline$ So, we set each factor equal to zero and solve for $x$ . $\newline$ $x - 5 = 0$ or $x + 1 = 0$
Solve for x: Solving the first equation for x gives us the first x-intercept: $\newline$ $x - 5 = 0$ $\newline$ $x = 5$
First x-intercept: Solving the second equation for x gives us the second x-intercept: $\newline$ $x + 1 = 0$ $\newline$ $x = -1$
Second x-intercept: We have found two x-intercepts: $(5, 0)$ and $(-1, 0)$ . These are the points where the parabola crosses the x-axis.