SOLUTION: it says, "Sketch the graphs, using the function and three points: two roots and the turning point. f(x)= x^2-2x-8 f(x)= x^2-2x-15

Algebra ->  Test -> SOLUTION: it says, "Sketch the graphs, using the function and three points: two roots and the turning point. f(x)= x^2-2x-8 f(x)= x^2-2x-15      Log On


   

Question 681992: it says, "Sketch the graphs, using the function and three points: two roots and the turning point.
f(x)= x^2-2x-8
f(x)= x^2-2x-15
Found 2 solutions by ReadingBoosters, MathLover1:
Answer by ReadingBoosters(3246) About Me  (Show Source):
You can put this solution on YOUR website!
f(x) = x%5E2-2x-8
=(x-4)(x+2)
roots/zeros/intercepts at 4 and -2
Plot (4, 0) and (-2, 0)
...
complete the square to find turning point
x^2 - 2x - 8 = 0
x^2 - 2x + 1 = 8 + 1
x^2 - 2x + 1 = 9
y = (x-1)^2 - 9
vertex/turning point at 1, -9
Plot (1,-9)
...
graph%28300%2C200%2C-10%2C10%2C-10%2C10%2Cx%5E2-2x-8%29
...
f(x) = x%5E2-2x-15
= (x-5)(x+3)
roots/zeros/intercepts at 5 and -3
Plot (5, 0) and (-3, 0)
...
complete the square to find the turning point
x^2 - 2x - 15 = 0
x^2 - 2x = 15
x^2 - 2x + 1 = 15 + 1
(x-1)^2 - 16 = 0
y = (x-1)^2 - 16
Plot (1,-16)
...
graph%28300%2C200%2C-10%2C10%2C-20%2C10%2Cx%5E2-2x-15%29
.....................
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Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
1.
f%28x%29=+x%5E2-2x-8...factor completely, replace -2x with 2x-4x
f%28x%29=+x%5E2%2B2x-4x-8.......group
f%28x%29=+%28x%5E2%2B2x%29-%284x%2B8%29
f%28x%29=+x%28x%2B2%29-4%28x%2B2%29
f%28x%29=+%28x-4%29%28x%2B2%29....set f%28x%29=0

0=+%28x-4%29%28x%2B2%29
if 0=+%28x-4%29..=>...x=4
if 0=+%28x%2B4%29..=>...x=-2

so, the roots are x=4 and x=-2
and points are (4,0) and (-2,0)
let x=1, solve for f%28x%29 and find third point

f%281%29=+1%5E2-2%2A1-8
f%281%29=+1-2-8
f%281%29=+-9
so, third point is (1,-9)
now, graph it




2.
f%28x%29=++x%5E2-2x-15...factor completely, replace -2x with 3x-5x
f%28x%29=+x%5E2%2B3x-5x-15.......group
f%28x%29=+%28x%5E2%2B3x%29-%285x%2B15%29
f%28x%29=+x%28x%2B3%29-5%28x%2B3%29
f%28x%29=+%28x-5%29%28x%2B3%29....set f%28x%29=0

0=+%28x-5%29%28x%2B3%29
if 0=+%28x-5%29..=>...x=5
if 0=+%28x%2B3%29..=>...x=-3

so, the roots are x=5 and x=-3
and points are (5,0) and (-3,0)
let x=1, solve for f%28x%29 and find third point

f%281%29=+1%5E2-2%2A1-15
f%281%29=+1-2-15
f%281%29=+-16
so, third point is (1,-16)
now, graph it