From f501256b8e5da4ed4ce500b277795fe2071947c9 Mon Sep 17 00:00:00 2001 From: James Su Date: Mon, 30 Dec 2019 02:35:44 +0000 Subject: [PATCH] Update Quadratic Equations.md --- .../Quadratic Equations.md | 8 ++------ 1 file changed, 2 insertions(+), 6 deletions(-) diff --git a/Grade 10/Math/MPM2DZ/Math Oral Presentation Questions/Quadratic Equations.md b/Grade 10/Math/MPM2DZ/Math Oral Presentation Questions/Quadratic Equations.md index 0b28236..b8b0d8f 100644 --- a/Grade 10/Math/MPM2DZ/Math Oral Presentation Questions/Quadratic Equations.md +++ b/Grade 10/Math/MPM2DZ/Math Oral Presentation Questions/Quadratic Equations.md @@ -121,6 +121,7 @@ $`\therefore`$ The $`x`$-intercepts are at $`\dfrac{2}{3}, \dfrac{-1}{4}`$ ### Question 3 c) When $`P(x) = 0`$, that means it is the break-even point for a value of $`x`$ (no profit, no loss). + $`2k^2 + 12k - 10 = 0 \implies k^2 -6k + 5 = 0`$ $`(k-5)(k-1) = 0`$ @@ -158,7 +159,7 @@ $`x = \dfrac{3 \pm \sqrt{23}}{7}`$ $`\because \dfrac{1}{3}`$ 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 gives those roots. -After expanind we get: +After expanding we get: $`y = x^2 - \dfrac{2}{3}x - \dfrac{1}{3}x + \dfrac{2}{3}`$ @@ -238,15 +239,10 @@ Since we know that $`(4, 5)`$ is also a point on the parabola, we can susbsitute $`5 = a + c \quad (2)`$ ```math - \begin{cases} - 9a + c = 0 & \text{(1)} \\ - a + c = 5 & \text{(2)} \\ - \end{cases} - ``` $`(2) - (1)`$