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.
