Question Find the x-intercepts of the function $y=-2(x-1)(x+5)$ .

Studdy Solution

STEP 1

Assumptions
1. The function given is $y = -2(x - 1)(x + 5)$ .
2. To find the $x$ -intercepts, we need to find the values of $x$ for which $y = 0$ .

STEP 2

Set the function equal to zero to find the $x$ -intercepts.
$0 = -2(x - 1)(x + 5)$

STEP 3

Since the product of the terms is zero, one or both of the terms must be zero. We can set each term equal to zero to find the $x$ -intercepts.
$x - 1 = 0 \quad \text{or} \quad x + 5 = 0$

STEP 4

Solve the first equation for $x$ .
$x - 1 = 0$ $x = 1$

STEP 5

Solve the second equation for $x$ .
$x + 5 = 0$ $x = -5$

STEP 6

The $x$ -intercepts are the points where $y = 0$ , which correspond to the $x$ -values we found.
The $x$ -intercepts are $(1, 0)$ and $(-5, 0)$ .

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Question Find the x-intercepts of the function $y=-2(x-1)(x+5)$ .

Studdy Solution

STEP 1

Assumptions
1. The function given is $y = -2(x - 1)(x + 5)$ .
2. To find the $x$ -intercepts, we need to find the values of $x$ for which $y = 0$ .

STEP 2

Set the function equal to zero to find the $x$ -intercepts.
$0 = -2(x - 1)(x + 5)$

STEP 3

Since the product of the terms is zero, one or both of the terms must be zero. We can set each term equal to zero to find the $x$ -intercepts.
$x - 1 = 0 \quad \text{or} \quad x + 5 = 0$

STEP 4

Solve the first equation for $x$ .
$x - 1 = 0$ $x = 1$

STEP 5

Solve the second equation for $x$ .
$x + 5 = 0$ $x = -5$

STEP 6

The $x$ -intercepts are the points where $y = 0$ , which correspond to the $x$ -values we found.
The $x$ -intercepts are $(1, 0)$ and $(-5, 0)$ .

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Question Find the x-intercepts of the function y=−2(x−1)(x+5)y=-2(x-1)(x+5)y=−2(x−1)(x+5).

Studdy Solution

STEP 1

Assumptions1. The function given is y=−2(x−1)(x+5) y = -2(x - 1)(x + 5) y=−2(x−1)(x+5).2. To find the x x x-intercepts, we need to find the values of x x x for which y=0 y = 0 y=0.

STEP 2

Set the function equal to zero to find the x x x-intercepts.0=−2(x−1)(x+5) 0 = -2(x - 1)(x + 5) 0=−2(x−1)(x+5)

STEP 3

Since the product of the terms is zero, one or both of the terms must be zero. We can set each term equal to zero to find the x x x-intercepts.x−1=0orx+5=0 x - 1 = 0 \quad \text{or} \quad x + 5 = 0 x−1=0orx+5=0

STEP 4

Solve the first equation for x x x.x−1=0 x - 1 = 0 x−1=0 x=1 x = 1 x=1

STEP 5

Solve the second equation for x x x.x+5=0 x + 5 = 0 x+5=0 x=−5 x = -5 x=−5

STEP 6

The x x x-intercepts are the points where y=0 y = 0 y=0, which correspond to the x x x-values we found.The x x x-intercepts are (1,0) (1, 0) (1,0) and (−5,0) (-5, 0) (−5,0).

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Question Find the x-intercepts of the function $y=-2(x-1)(x+5)$ .

Assumptions
1. The function given is $y = -2(x - 1)(x + 5)$ .
2. To find the $x$ -intercepts, we need to find the values of $x$ for which $y = 0$ .

Set the function equal to zero to find the $x$ -intercepts.
$0 = -2(x - 1)(x + 5)$

Since the product of the terms is zero, one or both of the terms must be zero. We can set each term equal to zero to find the $x$ -intercepts.
$x - 1 = 0 \quad \text{or} \quad x + 5 = 0$

Solve the first equation for $x$ .
$x - 1 = 0$ $x = 1$

Solve the second equation for $x$ .
$x + 5 = 0$ $x = -5$

The $x$ -intercepts are the points where $y = 0$ , which correspond to the $x$ -values we found.
The $x$ -intercepts are $(1, 0)$ and $(-5, 0)$ .