Let f(x)=25x2−2 . The function g(x) is a vertical stretch of f(x) by a factor of 2. What is the equation of g(x)?

Answer:  The required equation of g(x) is[tex]g(x)=50x^2-4.[/tex]Step-by-step explanation:   The given function is[tex]f(x)=25x^2-2~~~~~~~~~~~~~~~~~~(i)[/tex]The function g(x) is a vertical stretch of f(x) by a factor of 2.We are to find the equation of g(x).Since the co-efficient of x² in equation (i) is positive, so the parabola opens upward.So, the vertical stretch will be in the downward direction.Since g(x) is the vertical stretch of f(x) by 2, so we must have[tex]g(x)=2\times f(x)\\\\\Rightarrow g(x)=2(25x^2-2)\\\\\Rightarrow g(x)=50x^2-4.[/tex]Thus, the required equation of g(x) is[tex]g(x)=50x^2-4.[/tex]