The graphs below are both quadratic functions. The equation of the red graph isx)= x. Which of these is the equation of the blue graph, g(x)?

Answer:D. [tex]g(x)=\frac{1}{5}x^2[/tex]Step-by-step explanation:The equation of the red quadratic graph is [tex]f(x)=x^2[/tex].This is the parent quadratic function or the base of the quadratic functions.This red quadratic graph has been dilated by a certain scale factor  to obtain the blue graph. Recall that, when the scale factor is a fraction, such that [tex]0\:<\:k\:<\:1[/tex] the graph is stretched horizontally.The dilated graph then becomes wider than the parent function.From the given function equations, the possible value of k can only be [tex]k=\frac{1}{5}[/tex].Therefore the blue graph has equation: [tex]g(x)=\frac{1}{5}x^2[/tex]The correct answer is D.