Answer:
The vertex form is [tex]g(x)=-4x^2+5[/tex]
Step-by-step explanation:
Given : The parent function [tex]f(x)=x^2[/tex]
To reflect across the x-axis,
f(x) → - f(x)
[tex]f(x)=-x^2[/tex]
Vertically stretched by a factor of 4,
f(x) → a f(x)
[tex]f(x)=-4x^2[/tex]
Translated 5 units upward,
f(x) → f(x)+k
[tex]f(x)=-4x^2+5[/tex]
The required function is [tex]g(x)=-4x^2+5[/tex]
The general vertex form is [tex]g(x) =a(x - h)^2 + k[/tex]
Here, a=-4, h=0 and k=5
