color(green)("Method tutorial")
It is a quadratic curve (Horse shoe shape)
color(blue)("General shape")
The coefficient of x^2 is +1 -> positive
so the shape is U. If the coefficient had been negative it would have been the other way up ( nn)
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color(blue)("The y-intercept") is when x=0 so you can find it by substitution. (Tip: it is the constant!!!!)
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color(blue)("The x-intercept") is when y=0 so you can find this by factoring (much the quicker method) or using the formula:
Standard form equation of ax^2+bx+c=0
In conjunction with x= (-b+-sqrt(b^2-4ac))/(2a)
If the sqrt(b^2-4ac) bit is negative then the curve does not cross the x-axis and if you are determined to get some answers you have to use a branch of maths called Complex Numbers.
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color(blue)("Turning point of the curve (vertex)")
The Top/Bottom of the curve (maximum/minimum) is quite easy to find. Using the standard form equation. Change it to
y=a(x^2+b/ax) +c
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color(brown)("There another one you can use called vertex equation which has a"
color(brown)("different approach")
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In your case a=1 so b/a x ->color(blue)((-1)/1) x
color(green)(v_("vertex"))=(-1/2)xxcolor(blue)(b/a) -> (-1/2)xx(color(blue)(-1)) =color(green)(+1/2)
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color(green)(y_("vertex")) ->substitute the found value of color(green)(v_("vertex"))
![Tony B]()
