Quandaries and Queries
Secondary Level Questions
Is there a way to find the intersections of these graphs algebraically?
x2 + y = 4 & 2x - y = 1
I got (1.45, 1.9) and (-3.45, -7.9) with a graphing calculator.
y = 3.29x & y = 5.5(x0.5)+ 10000
I got x at 3133 with a graphing calculator.
First write the expressions in the form y = f(x) and y = g(x), that is
I plotted the two functions as you did and got
Look at one of the points where the graphs intersect and call it P. Suppose that the first coordinate of P is x.
Thus 4 - x2 = 2x - 1, that is x2 + 2x - 5 = 0. Solve for x. (This quadratic doesn't factor so you will need to use the general quadratic formula.)
For the second problem the technique is similar. Write the expressions in the form y = f(x) and y = g(x). Set f(x) = g(x) and solve for x.