# Calculus Slope Problem (Should be very easy!)

• Sep 21st 2013, 08:22 AM
Calculus Slope Problem (Should be very easy!)
Hi all,

I have the easiest problem ever...and yet I just can't solve it. It furstrates me to the point of wanting to punch the wall, because the problem itself looks so darn easy! It's a homework problem, and I've already done 20 or so problems that are much, much harder. And yet this one problem confounds me to the point of tears. Any help? (Crying)

Problem:

Find a function y = ax^2 + bx + c whose graph has an x-intercept of 1, a y-intercept of -2, and a tangent line with a slope of -1 at the y intercept.

My work so far:

At (0, -2), Y' = -X + 2

Thus, Y - -0.5X^2 + 2X + C

And C = -2 (Can be figured out from y-intercept)

But the equation I get isn't right...help :(
• Sep 21st 2013, 08:49 AM
HallsofIvy
Re: Calculus Slope Problem (Should be very easy!)
Quote:

Hi all,

I have the easiest problem ever...and yet I just can't solve it. It furstrates me to the point of wanting to punch the wall, because the problem itself looks so darn easy! It's a homework problem, and I've already done 20 or so problems that are much, much harder. And yet this one problem confounds me to the point of tears. Any help? (Crying)

Problem:

Find a function y = ax^2 + bx + c whose graph has an x-intercept of 1, a y-intercept of -2, and a tangent line with a slope of -1 at the y intercept.

My work so far:

At (0, -2), Y' = -X + 2

Thus, Y - -0.5X^2 + 2X + C

And C = -2 (Can be figured out from y-intercept)

So you are saying y= -(1/2)x^2+ 2x- 2. When x= 1, y(1)= -(1/2)+ 2- 2= -1/2, NOT 1 so this does not satisfy "has an x-intercept of 1".
Your mistake is saying that "at x= (0, -2), Y'= -x+ 2". The equation of the tangent line, at (0, -2), is y= -2x+ 2 but that is NOT the derivative function.

Quote:

But the equation I get isn't right...help :(
Instead, knowing that y= ax^2+ bx+ c, the fact that this function "has an x-intercept of 1" means that y(1)= a+ b+ c= 1. The fact that the graph has "a y-intercept of -2" means that y(0)= c= -2. The fact that the " tangent line with a slope of -1 at the y intercept" means that y'(0)= 2a(0)+ b= -2 so that b= -2. Put b= c= -2 into a+ b+ c= 1 to find a.
• Sep 21st 2013, 08:58 AM