Mathematics: Convert y-1=2(x-5) to slope intercept

Convert y-1=2(x-5) to slope intercept

Wolfgirl2032

17.03.2023

The x-intercepts are:

(1, 0)(2, 0)(6, 0)

The y-intercept is (-12, 0)

Step-by-step explanation:

Given the function

$f\left(x\right)=x^3-9x^2+\:20x\:-12$

Determining the x-intercepts and the y-intercept of the graph of f(x)

Finding x-intercept

We can determine the x-intercept by setting y = 0 and determining the corresponding value of x.

$y=x^3-9x^2+\:20x\:-12$

plug in x = 0

x^3-9x^2+20x-12=0

$(x-1) (x-2) (x-6) = x^3-9x^2+\:20x\:-12$

$\left(x-1\right)\left(x-2\right)\left(x-6\right)=0$

Using the zero factor principle

if ab = 0 then a=0 or b=0 (or both a=0 and b=0)

Thus,

$x-1=0\quad \mathrm{or}\quad \:x-2=0\quad \mathrm{or}\quad \:x-6=0$

$x=1,\:x=2,\:x=6$

Thus, the x-intercepts are:

(1, 0)(2, 0)(6, 0)

Finding y-intercept

We can determine the y-intercept by setting x = 0 and determining the corresponding value of y.

$y=x^3-9x^2+\:20x\:-12$

plug in y = 0

$y=\left(0\right)^3-9\left(0\right)^2+\:20\left(0\right)\:-12$

y=0-0+0-12

y=-12

Therefore, the y-intercept is (-12, 0)

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