Point of intersection coordinates (Diff)

Jun 2017
1
0
England
Hi, I'm revising for an upcoming calculus test and have a differentiation problem. A curve y=x^2 + x + 3 and line y = 2x + 5 are on a graph diagram (not to scale). I need to find the co ordinates for each two points of intersection on the graph.

I'm not sure whether I'd use the turning points method for maximum / minimum values? Or whether it's actually an integration problem?

With the turning point method would I first add both equations into one simultaneous equation 2x + 5 = x^2 + x + 3 differentiate that, rearrange and then factorise? Or rearrange, differentiate then factorise?

Thanks
 

skeeter

Math Team
Jul 2011
3,196
1,724
Texas
A curve y=x^2 + x + 3 and line y = 2x + 5 are on a graph diagram (not to scale). I need to find the co ordinates for each two points of intersection on the graph.
if the intersection(s) of the two functions are all that is required, then calculus is unnecessary ... just set the two functions equal to each other and solve for $x$ ...

$x^2+x+3 = 2x+5$

$x^2-x-2=0$

$(x-2)(x+1)=0$

$x=2 \implies y = 9$

$x=-1 \implies y = 3$