Question

The solid parabola descends through left parenthesis negative 4.5 comma 15 right parenthesis, continues through left parenthesis negative 4 comma 11 right parenthesis, passes through plotted and marked point left parenthesis negative 3 comma 4 right parenthesis, passes through the x-axis at left parenthesis negative 2.2 comma 0 right parenthesis, continues to descend to a valley at left parenthesis 0 comma negative 5 right parenthesis, turns and rises through left parenthesis 2.2 comma 0 right parenthesis, passes through plotted and marked point left parenthesis 4 comma 11 right parenthesis, and through left parenthesis 4.5 comma 15 right parenthesis. A dotted line intersects the parabola at the two plotted points at left parenthesis negative 3 comma 4 right parenthesis and left parenthesis 4 comma 11 right parenthesis. All values are approximate.

The functions of g(x)
and f(x)
are graphed. What is the larger solution in the solution set of f(x)=g(x)
?

Answer 1

The parabola has vertex (0,-5) and passes through (-3,4), so f(x)=x^2-5. The dotted line through (-3,4) and (4,11) is g(x)=x+7. Solve x^2-5 = x+7 → x^2-x-12=0 → (x-4)(x+3)=0. The larger solution is x = 4.