Algebra Pre-Algebra and Basic Algebra Math Forum

 February 9th, 2018, 10:43 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 02:46 AM.
 February 9th, 2018, 10:55 PM #2 Senior Member   Joined: Feb 2016 From: Australia Posts: 1,737 Thanks: 606 Math Focus: Yet to find out. Can you upload the image? Thanks from greg1313
 February 10th, 2018, 02:59 AM #3 Global Moderator   Joined: Dec 2006 Posts: 19,974 Thanks: 1850 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, 10:22 AM #4 Newbie   Joined: Dec 2017 From: Spain Posts: 18 Thanks: 1 The parabola intersects the x-Axis 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 (-2|0). 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 y-Axis at y=(-2), the new function looks like that: g(x)=m*x-2 Since we know the points P(-2|0) and Q(0|-2), 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)=-x-2 Thus the line g intersects the parabola at (3|-5) We are now looking for the function of the perpendicular line h to line g through (3|-5). 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 y-Axis at (0|-8) (-5-3=-8). Finally, having the line h's function (h(x)=x-8) we can calculate the zero point of the function: 0=x-8 /+8 8=x Hence, the zero point stays at Z(8|0), which is the sought point. Hope you like the explanation. Last edited by skipjack; February 10th, 2018 at 03:11 PM. Reason: to disable smilies
 February 10th, 2018, 10:24 AM #5 Newbie   Joined: Dec 2017 From: Spain Posts: 18 Thanks: 1 All the smilies stay for -8

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