Eric Nicholas K's answer to Kathy's Secondary 4 A Maths Singapore question.
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Q34a, Q34b
I always change all sad face graphs to smiley face graphs so I only need to remember one kind of graph. In other words, I make sure one side is zero and the other side has a positive coefficient of x2.
I always change all sad face graphs to smiley face graphs so I only need to remember one kind of graph. In other words, I make sure one side is zero and the other side has a positive coefficient of x2.
Date Posted:
4 years ago
How or when will I know to draw the line outside or inside the u shape
For your discriminants b2 - 4ac which reduce to inequalities such as this one, the graph of the b2 - 4ac (to be distinguished from the graph of the actual curve) must cut the “horizontal axis”.
So let’s say you obtain k2 - 2k - 3 > 0 as the inequality and you are solving for it.
This graph will definitely cut the horizontal 0, so we factorise into (k - 3) (k + 1) and shade the appropriate region.
This graph will definitely cut the horizontal 0, so we factorise into (k - 3) (k + 1) and shade the appropriate region.
I mean the shade the part
Always convert your quadratic inequality into positive coefficients of x2 so you will remember the u-shaped graph only. Remembering the n-shaped graph can cause confusion.
Above the horizontal line is the region “> 0”.
Below the horizontal line is the region “< 0”.
Below the horizontal line is the region “< 0”.
So let’s say (k - 3) (k + 1) > 0.
We draw the u-shaped graph passing -1 and 3.
The parts above the line (k < -1 and k > 3) are to be shaded, since for these values of k, the value of (k - 3) (k + 1) are positive after substitution of k.
We draw the u-shaped graph passing -1 and 3.
The parts above the line (k < -1 and k > 3) are to be shaded, since for these values of k, the value of (k - 3) (k + 1) are positive after substitution of k.
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