A question to do with graphical solutions of equations.
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A question to do with graphical solutions of equations.

[From: ] [author: ] [Date: 11-10-17] [Hit: ]
..how?! Thanks! Oh and pls dont use complex methods such as equations coz i havent done that yet.......
Assuming the graph of y=x²-8x-7 has been drawn, find the equation of the line which should be drawn to solve the equation 2x²=16x+2

I tried so many times but i keep getting it wrong! The answer is y= -2.5....how?! Thanks! Oh and pls don't use complex methods such as equations coz i haven't done that yet... i'm in year 11 (15 years old)

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Hello,

You have drawn the graph defined by
y = x² - 8x - 7

= = = = = = = = = = = = = = = = = = = = = =
And you want to solve graphically
2x² = 16x + 9

Let manipulate the equation to solve:
2x² = 16x + 9
x² = 8x + 9/2
x² - 8x - 9/2 = 0
x² - 8x - 7 + 5/2 = 0

But that "x²-8x-7"... Does it ring a bell? Isn't it "y" in the graphed expression?
Let's replace this by y and we get:
y + 5/2 = 0
y = -5/2 (and you get your answer...)

Hence if we graph the horizontal line y=-5/2, the line crosses the graph of y=x²-8x-7 in two points, whose respective x-coordinates will be the solutions.

= = = = = = = = = = = = = = = = = = = = = =
You want to solve graphically
x² = 7

Let manipulate the equation to solve:
x² = 7
x² - 7 = 0
x² - 8x - 7 + 8x = 0

Guess what to do now with that "x²-8x-7" ?
y + 8x = 0
y = -8x

Hence if we graph the oblique line y=-8x, the line crosses the graph of y=x²-8x-7 in two points, whose respective x-coordinates will be the solutions.

= = = = = = = = = = = = = = = = = = = = = =
Logically,
Dragon.Jade :-)
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