Question

The graphs below are both quadratic functions. The equation of the red graph is

x)= x. Which of these is the equation of the blue graph, g(x)?

Answer 1

D.
`g(x)=(1)/(5)x^2`

Explanation:

• The equation of the red quadratic graph is
  `f(x)=x^2`.
• 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
  `0\:<\:k\:<\:1` 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
  `k=(1)/(5)`.
• Therefore the blue graph has equation:
  `g(x)=(1)/(5)x^2`
• The correct answer is D.