graph the equation y=x²- 6x - 8. you must plot five points including the roots and the vertex

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30-10-2022
Mathematics

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graph the equation y=x²- 6x - 8. you must plot five points including the roots and the vertex

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AiyonnaC498705 AiyonnaC498705 · Answer 1 · 2022-10-30T01:56:26+02:00

graph the equation y=x²- 6x - 8. you must plot five points including the roots and the vertex

we have the equation

[tex]y=x^2-6x-8[/tex]

this is a quadratc equation (vertical parabola) open upward (because the leading coefficient is positive)

step 1

Find the vertex

Convert the equation into vertex form

y=a(x-h)^2+k

where

(h,k) is the vertex

Complete the squares

[tex]\begin{gathered} y=x^2-6x-8 \\ y=(x^2-6x)-8 \\ y=(x^2-6x+9-9)-8 \\ y=(x^2-6x+9)-8-9 \\ y=(x^2-6x+9)-17 \\ y=(x-3)^2-17 \end{gathered}[/tex]

the vertex is the point (3,-17)

step 2

Find the y-intercept

value of y when the value of x is zero

For x=0

y=(0-3)^2-17

y=9-17

y=-8

the y-intercept is (0,-8)

step 3

Find the roots

The roots are the values of x when the value of y is zero

so

For y=0

[tex]\begin{gathered} 0=(x-3)^2-17 \\ (x-3)^2=17 \\ x-3=\pm\sqrt[\square]{17} \\ x=3\pm\sqrt[\square]{17} \end{gathered}[/tex]

therefore

the roots are

[tex](3+\sqrt[,]{17},0)[/tex]

and

[tex](3-\sqrt[,]{17},0)[/tex]

Simplify

(7.12,0) and (-1.12,0)

step 4

Plot the given points to graph the given function

using a graphing tool

see the attached figure

please wait a minute to plot the points