# differential calculus

• Feb 16th 2008, 04:16 AM
fiordalisa
differential calculus
Hi everyone!
I know this is probably a pretty easy question but I'm having a mental block at the minute...
Anyway the question is: "Show that the curves C1 and C2 intersect at the points (-2,16) and (1,7)"
C1 : y= -x^2 - 4x +12
C2 : y= 5x^2 + 2x

N.B. I'm new to the forums and wasn't sure how to write "squared" so in case I got it wrong "^2" = squared

• Feb 16th 2008, 04:31 AM
angel.white
Quote:

Originally Posted by fiordalisa
Hi everyone!
I know this is probably a pretty easy question but I'm having a mental block at the minute...
Anyway the question is: "Show that the curves C1 and C2 intersect at the points (-2,16) and (1,7)"
C1 : y= -x^2 - 4x +12
C2 : y= 5x^2 + 2x

N.B. I'm new to the forums and wasn't sure how to write "squared" so in case I got it wrong "^2" = squared

If they intersect, they will have the same x value and y value (see attached graph of the two functions.) So plug the x value into both equations, if they have the same y value, then they intersect at that point.

Test x=-2
$\begin{array}{rl}C1: y&= -(-2)^2 - 4(-2) +12\\
&= -(4) - (-8) +12\\
&= -4 + 8 +12\\
&= 16\\\end{array}$

$\begin{array}{rl}C1: y&= 5(-2)^2 + 2(-2)\\
&= 5(4) + (-4)\\
&= 20 -4\\
&= 16\\\end{array}$

Therefore they each pass through the point (-2,16) And thus intersect at that point.

You try the second one.
• Feb 16th 2008, 03:54 PM
xifentoozlerix
Quote:

Originally Posted by fiordalisa
Hi everyone!
I know this is probably a pretty easy question but I'm having a mental block at the minute...
Anyway the question is: "Show that the curves C1 and C2 intersect at the points (-2,16) and (1,7)"
C1 : y= -x^2 - 4x +12
C2 : y= 5x^2 + 2x

N.B. I'm new to the forums and wasn't sure how to write "squared" so in case I got it wrong "^2" = squared

When you want to find the intersection of two functions, you can set them equal to each other and solve for x. Then plug the x values you get back into either original function and you will get your y values.

y= -x^2 - 4x +12
y= 5x^2 + 2x

both equal y, so make them equal to each other:
-x^2 - 4x +12 = 5x^2 + 2x

collect like terms on one side:
-6x^2-6x+12=0

now factor:
-6(x^2+x-2)=0
x^2+x-2=0
(x+2)(x-1)=0
x=-2 or x=1

....then plug in.