Posted by **mike** on Thursday, November 22, 2012 at 9:43pm.

Find the values of a,b, and c if the parabola y=a(x^2)+bx+c is tangent to the line y=-2x+3 at (2,-1) and has a critical point when x=3

- math -
**Steve**, Friday, November 23, 2012 at 5:16am
y' = 2ax + b

we want y'(3) = 0, so

6a+b = 0

the line -2x+3 has slope -2, so

we want y'(2) = -2, so

4a+b = -2

and we have (a,b) = (1,-6)

y = x^2 - 6x + c

We know that y(2) = -1, so

-1 = 4 - 12 + c

so, c = 7

y = x^2 - 6x + 7

## Answer This Question

## Related Questions

- math - The line x=c where c>0 intersects the cubic y=2x^(3)+3x^(2)-9 at point...
- Math - If f(x)=3x^2-5x, find the f'(2) & use it to find an equation of tangent ...
- calculus - The line x=c where c>0 intersects the cubic y=2x^(3)+3x^(2)-9 at ...
- Math - Let f(x) be the parabola -x^2+16x-16. find the point (x,y) on f such that...
- Calculus - Sketch a graph of the parabola y=x^2+3. On the same graph, plot the ...
- Calc. - Find the area of the region bounded by the parabola y=x^2, the tangent ...
- math - Consider the parabola y = 7x - x2. (a) Find the slope of the tangent line...
- calc - for the parametric curve defined by x=3-2t^2 and y=5-2t ...sketch the ...
- maths - find the gradient of the tangent to the parabola y=4x-x^2 at (0,0) hence...
- math help - find the equation to the tangent line of the parabola given by x^2=...

More Related Questions