# [SOLVED] Quadratics and Co-ordinate Geometry

• Oct 3rd 2009, 08:03 AM
unstopabl3
[SOLVED] Quadratics and Co-ordinate Geometry
The equation of the curve is $\displaystyle y=8x-x^2$

Q) Find the coordinates of the stationary point of the curve.

I know that I am supposed to express this equation in the form $\displaystyle a-(x+b)^2$ and then get the values of b for x and a for y to get the answer. But what are stationary points? Is that the vertex?

Q) Find the set of values of x for which y is greater than equal to -20

I've got the final answer

(x+2)(x-10) is less than or equal to 0

x= -2 or x= 10

Now what I don't understand is what is the sketch method? And how to easily find out which of the two (-2 or 10) is less than or equal to x or which one is greater than or equal to x.

Thanks a lot in advance.
• Oct 3rd 2009, 08:14 AM
Quote:

Originally Posted by unstopabl3
The equation of the curve is $\displaystyle y=8x-x^2$

Q) Find the coordinates of the stationary point of the curve.

I know that I am supposed to express this equation in the form $\displaystyle a-(x+b)^2$ and then get the values of b for x and a for y to get the answer. But what are stationary points? Is that the vertex?

Q) Find the set of values of x for which y is greater than equal to -20

I've got the final answer

(x+2)(x-10) is less than or equal to 0

x= -2 or x= 10

Now what I don't understand is what is the sketch method? And how to easily find out which of the two (-2 or 10) is less than or equal to x or which one is greater than or equal to x.

Thanks a lot in advance.

HI

(1) You can use differentiation or complete the square like you did . Yes , its vertex .. or in other words max or min points .

(2) Ok .. $\displaystyle (x-10)(x+2)\leq0$

You will get a U shaped graph where it intersects x=10 and x=-2 .

y is less than or equals 0 ... so the solution part will be the lower part of the U graph because the lower part of the graph has all its values of y lesser than 0 ..

Did i make things confusing for you ?
• Oct 3rd 2009, 08:47 AM
unstopabl3
Thanks for the quick reply, I am still confused about Q#2

Can you please explain a bit more on how to find out which of the two (-2 or 10) is less than or equal to x or which one is greater than or equal to x. Do you understand what I mean?
• Oct 3rd 2009, 10:49 PM
Quote:

Originally Posted by unstopabl3
Thanks for the quick reply, I am still confused about Q#2

Can you please explain a bit more on how to find out which of the two (-2 or 10) is less than or equal to x or which one is greater than or equal to x. Do you understand what I mean?

Do you know how to sketch the graph ? When the inequality is $\displaystyle \leq0$ or $\displaystyle <0$, then the solution will be the bottom part of the graph and if the inequality is $\displaystyle \geq0$ or $\displaystyle >0$ , then the solution will be the top part of the graph .

If you still don get me , then this is an alternative method .

since the inequality is $\displaystyle \leq 0$ , then one of the factors must be negative and the other one will be positive . Since you do not know which is which , so you will need to solve for 2 cases .. ie

$\displaystyle x-10\leq0$ , $\displaystyle x+2\geq0$ --- case 1

$\displaystyle x-10\geq0$ , $\displaystyle x+2\leq 0$ --- case 2

Then draw a number line with these points and find the intersection .
• Oct 3rd 2009, 11:05 PM
unstopabl3
Thanks, I got it now ;)
Really appreciate you 'dumbing' it down for me :D