February 9th, 2018, 09:43 PM  #1 
Newbie Joined: Feb 2018 From: Afghanistan Posts: 17 Thanks: 0  Quadratics Find the coordinate of point A in the figure. Can you solve it in a way that doesn't involve derivation? Please solve step by step. Last edited by skipjack; February 10th, 2018 at 01:46 AM. 
February 9th, 2018, 09:55 PM  #2 
Senior Member Joined: Feb 2016 From: Australia Posts: 1,579 Thanks: 541 Math Focus: Yet to find out. 
Can you upload the image?

February 10th, 2018, 01:59 AM  #3 
Global Moderator Joined: Dec 2006 Posts: 18,845 Thanks: 1567 
You were mistyping the image address. If you pasted it, check what was pasted. I've corrected it for you. As the blue line through the points (2, 0) and (0,2) has equation y = x  2, it intersects the parabola at the point (3, 5). Hence the dotted line through A has equation y = x  8, which implies that A is the point (8,0). 
February 10th, 2018, 09:22 AM  #4 
Newbie Joined: Dec 2017 From: Spain Posts: 15 Thanks: 1 
The parabola intersects the xAxis at: f(x)=(x^2)+4 0=(x^2)+4 /4 4=(x^2) /√ ±2=x Since we are looking for the left zero point, it has to be deduced that the left zero point has the coordinate (20). Now, in order to deduce how the line's function looks like, we'll use the general function for lines: g(x)=m*x+n Since the line intersects the yAxis at y=(2), the new function looks like that: g(x)=m*x2 Since we know the points P(20) and Q(02), the slope will be, 2/2=1 and because the tendency is negative, the slope is 1. Hence the function of the line g is g(x)=x2 Thus the line g intersects the parabola at (35) We are now looking for the function of the perpendicular line h to line g through (35). Two lines are perpendicular if the slope of the first one equals the negative inverse of the second slope: m1=(1/m2) Thus the line h's slope will be 1{=[1/(1)]} Having the slope, we can deduce that the line h will intersect the yAxis at (08) (53=8). Finally, having the line h's function (h(x)=x8) we can calculate the zero point of the function: 0=x8 /+8 8=x Hence, the zero point stays at Z(80), which is the sought point. Hope you like the explanation. Last edited by skipjack; February 10th, 2018 at 02:11 PM. Reason: to disable smilies 
February 10th, 2018, 09:24 AM  #5 
Newbie Joined: Dec 2017 From: Spain Posts: 15 Thanks: 1 
All the smilies stay for 8


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