Determine the x-intercepts of the following equation. (x+3)(-x+4)=y (0,-3) and (0,4) (12,0) (-3,0) and (-4,0) (0,12) (-3,0) and (4,0) (0,-12)

Definition of x-intercepts: Understand the definition 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. Since y represents the height above the x-axis, we set y to 0 to find the x-intercepts. 0 = (x+3)(-x+4)Solve for x: Solve the equation for x. 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 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 + 3 = 0 or -x + 4 = 0Solve first equation: Solve the first equation for x. x + 3 = 0 x = -3Solve second equation: Solve the second equation for x. -x + 4 = 0 -x = -4 x = 4Combine results: Combine the results to find the x-intercepts. The x-intercepts are the solutions to the equations from Steps 4 and 5, which are x = -3 and x = 4.

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Determine the
x-intercepts of the following equation.

(x+3)(-x+4)=y

(0,-3) and
(0,4)

(12,0)

(-3,0) and
(-4,0)

(0,12)

(-3,0) and
(4,0)

(0,-12)

Determine the $x$ -intercepts of the following equation. $\newline$ $(x+3)(-x+4)=y$ $\newline$ $(0,-3)$ and $(0,4)$ $\newline$ $(12,0)$ $\newline$ $(-3,0)$ and $(-4,0)$ $\newline$ $(0,12)$ $\newline$ $(-3,0)$ and $(4,0)$ $\newline$ $(0,-12)$

View step-by-step help

Home

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+3)(-x+4)=y

\newline

(0,-3)

and

(0,4)

\newline

(12,0)

\newline

(-3,0)

and

(-4,0)

\newline

(0,12)

\newline

(-3,0)

and

(4,0)

\newline

(0,-12)

Definition of $x$ -intercepts: Understand the definition of $x$ -intercepts. $\newline$ 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. $\newline$ Since $y$ represents the height above the x-axis, we set $y$ to $0$ to find the x-intercepts. $\newline$ $0 = (x+3)(-x+4)$
Solve for x: Solve the equation for x. $\newline$ 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 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: $\newline$ $x + 3 = 0$ or $-x + 4 = 0$
Solve first equation: Solve the first equation for $x$ . $x + 3 = 0$ $x = -3$
Solve second equation: Solve the second equation for $x$ . $-x + 4 = 0$ $-x = -4$ $x = 4$
Combine results: Combine the results to find the $x$ -intercepts. The $x$ -intercepts are the solutions to the equations from Steps $4$ and $5$ , which are $x = -3$ and $x = 4$ .