[Video] Q13: The functions f and g, defined by f(x) = 8x^2 -2 and g(x) = -8x^2 +2, are graphed in the xy-plane above. the graphs of f and g intersect at the points (k,0) and (-k, 0). what is the value of k?

Explanation for Question 13 From the Math (No Calc) Section on the Official Sat Practice Test 4

Now on number 13, we have two graphs, 2 right? We have at them, we have a G and then they also give 3 us the equations of F and G. 4 And so here they are graphed in our, in our page. 5 And then they tell us that we have two intersection points, 6 K comma, zero and negative K commons Europe. 7 And we need to figure out what is the value of K. 8 And so the key here, right, is to realize that intersection points are 9 really what we call solutions solutions 10 to systems of equations. 11 So intersection points, our solutions, 12 and our two equations are F of X is equal to eight X squared 13 minus two, and G of X is equal to negative eight X squared plus 14 two. 15 So remember, whenever you have something of X and F of X, 16 of G of X, even in H of X, that's essentially a fancy way 17 of saying Y. So what I can do now to solve the systems of 18 equations, so I can get my solutions and solve for K, 19 um, is take this Y and plug it in here, 20 set I'm equal to each other, really, and then solve for X. 21 And it's important to know that, you know, you see a K it's an 22 X part of our, or ordered pairs. 23 So really our X here that we're solving for is a K not an 24 X, right? So I'm going to set these equal to each other because I'm 25 essentially substituting in the wise that way. 26 So I've got eight K squared minus two is equal to negative eight K 27 squared plus two. So I'll add eight K squared to both sides. 28 That way these eight K squares will cancel and I'll get the two is...