SOLUTION: Express 3+9x-x^2 in the form of q-(x+r)^2,where q and r are constants.Hence (a)sketch it's extreme value and the value of x when this occurs, (b)sketch the curve y=3+9x-x^2 I

Question 818813: Express 3+9x-x^2 in the form of q-(x+r)^2,where q and r are constants.Hence
(a)sketch it's extreme value and the value of x when this occurs,
(b)sketch the curve y=3+9x-x^2
I have found the values of q and r,but do not know what is extreme value and what does it mean.Please Help.
Answer by fcabanski(1391) (Show Source): You can put this solution on YOUR website!
The curve is a parabola. The x-coordinate of the parabola's vertex (the extreme value other than the extremes at the end (+ or - infinity) is given by -b/2a where a is the coefficient of the term and b is the coefficient of the x term.

For this equation a = -1 and b = 9 (c=3, but we won't use it until later). -b/2a = -9/-2 = 9/2.

Plug it back into the equation to find the y coordinate.

3+9*9/2-81/4 = 93/4. The vertex is (9/2,93/4).

Find the x - intercepts, where the parabola crosses the x-axis, using the quadratic equation = = = approximately -.322 and 9.270.

Plot the vertex and the intercepts. Draw the curve.

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