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Update Quadratic Equations.md
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@ -121,6 +121,7 @@ $`\therefore`$ The $`x`$-intercepts are at $`\dfrac{2}{3}, \dfrac{-1}{4}`$
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### Question 3 c)
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When $`P(x) = 0`$, that means it is the break-even point for a value of $`x`$ (no profit, no loss).
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$`2k^2 + 12k - 10 = 0 \implies k^2 -6k + 5 = 0`$
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$`(k-5)(k-1) = 0`$
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@ -158,7 +159,7 @@ $`x = \dfrac{3 \pm \sqrt{23}}{7}`$
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$`\because \dfrac{1}{3}`$ and $`\dfrac{-2}{3}`$ are the roots of a quadratic equation, that must mean that $`(x-\dfrac{1}{3})(x-\dfrac{2}{3})`$ is a quadratic equation that
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gives those roots.
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After expanind we get:
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After expanding we get:
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$`y = x^2 - \dfrac{2}{3}x - \dfrac{1}{3}x + \dfrac{2}{3}`$
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@ -238,15 +239,10 @@ Since we know that $`(4, 5)`$ is also a point on the parabola, we can susbsitute
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$`5 = a + c \quad (2)`$
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```math
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\begin{cases}
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9a + c = 0 & \text{(1)} \\
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a + c = 5 & \text{(2)} \\
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\end{cases}
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```
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$`(2) - (1)`$
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