I require some assistance with this graphing question, please.
2 answers:
Answer:
y-int = 5
roots: sqrt(5)-3 or -3 - sqrt(5)
TP @ (-3,5)
Step-by-step explanation:
y intercept = 5 (when x = 0)
Roots:
When y = 0
5 - (x + 3)^2 = 0
(x+3)^2 = 5
Square both sides:
x + 3 = Sqrt[5] or x + 3 = - Sqrt[5]
x = Sqrt[5] - 3 or x= - 3 - Sqrt[5]
Turning point (Critical Point):
dy/dx (5-(x+3)^2) = - 2 (x+3)
Solve -2 (x+3) = 0
x = - 3
y = 5
Max point at (-3,5)
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Slope-intercept form:
y = mx + b "m" is the slope, "b" is the y-intercept
For lines to be perpendicular, their slopes have to be the opposite/negative reciprocals (flipped sign and number)
For example:
slope is 2
perpendicular line's slope is -1/2
slope is -2/3
perpendicular line's slope is 3/2
3.) y = 2x - 2
The given line's slope is 2, so the perpendicular line's slope is -1/2
To find "b", plug in the point (-5 , 5) into the equation
Subtract 5/2 on both sides
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4.) -6x + 5y = -10 Get "y" by itself, add 6x on both sides
5y = -10 + 6x Divide 5 on both sides
The given line's slope is 6/5, so the perpendicular line's slope is -5/6.
Plug in (-2, 5)
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7.) Perpendicular line's slope is -2
y = -2x + b Plug in (1,4)
4 = -2(1) + b
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8.) Perpendicular line's slope is -1/4
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