Determine the x-intercepts of the following equation. (x+5)(x-4)=y (0,-5) and (0,4) (0,-20) (-5,0) and (-4,0) (-5,0) and (4,0) (0,20) (-20,0)

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.Solve for x: Set y to 0 in the equation (x+5)(x-4)=y to find the x-intercepts. 0 = (x+5)(x-4) Now we need to solve for x.Apply zero product property: The equation 0 = (x+5)(x-4) is already factored, so we can use the zero product property, which states that if a product of two 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+5 = 0 or x-4 = 0Solve x+5=0: Solve the first equation x+5 = 0 for x: x = -5Solve x-4=0: Solve the second equation x-4 = 0 for x: x = 4Find x-intercepts: The solutions to the equations x+5 = 0 and x-4 = 0 give us the x-intercepts of the parabola. Therefore, the x-intercepts are (-5,0) and (4,0).

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Determine the
x-intercepts of the following equation.

(x+5)(x-4)=y

(0,-5) and
(0,4)

(0,-20)

(-5,0) and
(-4,0)

(-5,0) and
(4,0)

(0,20)

(-20,0)

Determine the $x$ -intercepts of the following equation. $\newline$ $(x+5)(x-4)=y$ $\newline$ $(0,-5)$ and $(0,4)$ $\newline$ $(0,-20)$ $\newline$ $(-5,0)$ and $(-4,0)$ $\newline$ $(-5,0)$ and $(4,0)$ $\newline$ $(0,20)$ $\newline$ $(-20,0)$

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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-4)=y

\newline

(0,-5)

and

(0,4)

\newline

(0,-20)

\newline

(-5,0)

and

(-4,0)

\newline

(-5,0)

and

(4,0)

\newline

(0,20)

\newline

(-20,0)

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 $0$ .
Solve for x: Set $y$ to $0$ in the equation $(x+5)(x-4)=y$ to find the x-intercepts. $\newline$ $0 = (x+5)(x-4)$ $\newline$ Now we need to solve for $x$ .
Apply zero product property: The equation $0 = (x+5)(x-4)$ is already factored, so we can use the zero product property, which states that if a product of two 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 $x$ : $\newline$ $x+5 = 0$ or $x-4 = 0$
Solve $x+5=0$ : Solve the first equation $x+5 = 0$ for $x$ : $x = -5$
Solve $x-4=0$ : Solve the second equation $x-4 = 0$ for $x$ : $x = 4$
Find x-intercepts: The solutions to the equations $x+5 = 0$ and $x-4 = 0$ give us the x-intercepts of the parabola. Therefore, the x-intercepts are $(-5,0)$ and $(4,0)$ .