Determien the resulting function of the line with points (1,2) and (3,3) and

AI Thread Summary
To determine the resulting function of the line through points (1,2) and (3,3) and its intersection with f(x) = 2x^2 + 9, the line's equation is found to be y = 1/2x + 3/2. The user attempts to set this equal to the quadratic function to find intersections, leading to the equation -2x^2 + 1/2x + 21/2 = 0. However, there are errors in the algebra, as the resulting quadratic does not intersect the x-axis, indicating no real solutions. Clarifications on the calculations are requested to ensure accurate results.
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Determien the resulting function of the line with points (1,2) and (3,3) and...

Homework Statement




hi guys how are you, i am having a little trouble solving the question adn was wondering if some of you could give me a hand?

Determine the resulting function of the line with points (1,2) and (3,3) and f(x) = 2x^2 + 9 intersect?

Homework Equations





The Attempt at a Solution



Now idk how to solve this as its been a while since i did any math but i tried to put it into an equation of a line and i got y=1/2x+3/2 but i know that's not right as its for an equation of a line =/. I know i need to use the two points to make an equation and then do this

equation = 2x^2 + 9 but i don't know how to solve the two points and get an equation.
 
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Sorry if I'm being obtuse, but are trying to find the intersection between the line with points (1,2) and (3,3) and the function f(x) = 2x2 + 9? If so, you've gotten the equation for the line correct, now all you would need to do is solve for the intersections. If I've misinterpretted the question, hopefully you wouldn't mind clarifying for me.
 


I am trying to find the intersection so i guess i am right. So i woudl do this right?

1/2x + 3/2 = 2x^2 + 9

and that would result to

-2x2 + 1/2x + 21/2 = 0

Is this correct? Also could you see if this is correct as well?

I am given a y-intercept of 0 and a point of (2,2) and the equation of the line i got is this

y = 1x + 0

is that correct?
 
Last edited:


Well, your new quadratic equation isn't quite right (check the algebra)! The equation that you should get never intersects the x-axis. What does this suggest?
 


why not? what's wrong with it? which one are u referring too?
 


ohh i think you are right, should it be - 22 + 1/2x - 15/2 ??
 

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