Question

Approximate the solution of the system to the nearest thousandth.

y= -4x^2 + 5x + 1
y= -3^x

i only got this far:
-4x^2 + 5x + 1 = -3^x

please help! thanks :)

Answer 1

(-0.283, -0.733)

Explanation:

There are various ways in which to approximate the solution. One is to use a graphing calculator and graph the two functions separately, then determine the point of intersection. The first function has a parabolic graph that opens down, whereas the second function has an exponential graph which heads downward as x increases.

At first try I found that the two graphs intersect in Quadrant III, at approximately (-1/2, -3/4).

Next I used my calculator's CALC tools, specifically that which finds the coordinates of the intersection of two graphs, ending up with these coordinates: (-0.283, -0.733). These coordinates are to the nearest thousandths.

If and when you take Calculus, you'll learn Newton's Method for Finding Roots, which doesn't require a graphing calculator.