ai93
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a) Find the roots of the equation $$x^{2}+5x-6$$
b) Sketch the graph of the function $$x^{2}+5x-6$$ labeling the points at which the graph crosses the axes and the co-ordinates of the maximum and minimum of the curve
c) Find the equation of the tangent at the point where $$x=2$$ on the curve of $$y=x^{2}+5x-6$$
MY SOLUTION Right so far?
a) Using the quadratic formula, we get $$x=\frac{-5\pm\sqrt{49}}{2}$$
$$\therefore x=6$$ or $$-1$$
b)
$$y=x^{2}+5x-6$$
$$\d{y}{x}$$ = $$2x+5$$
$$x=-\frac{5}{2}$$ (-2.5)
Sub x into equation
$$y=(-\frac{5}{2})^{2}+5(-\frac{5}{2})-6$$
y=$$-\frac{49}{4}$$ (-12.25)
and $$\d{y^{2}}{^{2}x}$$ = 2 which is a minimum value
So with the graph, you would plot it with the parabola going with the x points -3 and 6 and the y points $$-\frac{49}{4}$$
c) No clue!
b) Sketch the graph of the function $$x^{2}+5x-6$$ labeling the points at which the graph crosses the axes and the co-ordinates of the maximum and minimum of the curve
c) Find the equation of the tangent at the point where $$x=2$$ on the curve of $$y=x^{2}+5x-6$$
MY SOLUTION Right so far?
a) Using the quadratic formula, we get $$x=\frac{-5\pm\sqrt{49}}{2}$$
$$\therefore x=6$$ or $$-1$$
b)
$$y=x^{2}+5x-6$$
$$\d{y}{x}$$ = $$2x+5$$
$$x=-\frac{5}{2}$$ (-2.5)
Sub x into equation
$$y=(-\frac{5}{2})^{2}+5(-\frac{5}{2})-6$$
y=$$-\frac{49}{4}$$ (-12.25)
and $$\d{y^{2}}{^{2}x}$$ = 2 which is a minimum value
So with the graph, you would plot it with the parabola going with the x points -3 and 6 and the y points $$-\frac{49}{4}$$
c) No clue!