Answer:
Step-by-step explanation:
Parent function for the given graph is,
f(x) = x²
1). When the given function is inverted or reflected across x-axis,
h(x) = -ax² [Since parabola is opening downwards]
2). Further the given graph is shifted 1 units left horizontally and 2 units down.
p(x) = -a(x + 1)² - 2
Therefore, there is a translation of 1 units towards left and 2 units down.
3). Since, the transformed function passes through (1, -4).
p(1) = -a(1 + 1)²- 2
-4 = -a(2)² - 2
-4 = -4a - 2
4a = 2
a = [tex]\frac{1}{2}[/tex]
Therefore, [tex]g(x)=\frac{1}{2}[p(x)][/tex]
Which shows a horizontal stretch of the function 'p' by a scale factor of [tex]\frac{1}{2}[/tex].
