Answer :
Answer:
Step-by-step explanation:
Equation of a parabola is represented by,
f(x) = -a(x - h)² + k [Parabola opening downwards]
where (h, k) is the vertex of the parabola.
Picture attached shows the vertex as (-1, -2)
Therefore, equation of the transformed parabola will be,
f(x) = -a(x + 1)²- 2
Since the given parabola passes through a point (1, -3)
-3 = -a(1 + 1)² - 2
-1 = -4a²
a = [tex]\sqrt{\frac{1}{4} }[/tex]
a = [tex]\frac{1}{2}[/tex]
Therefore, equation of the transformed function will be,
f(x) = [tex]-\frac{1}{2}(a+1)^2-2[/tex]
If the original or parent function is g(x) = x²,
Transformed function will have the following characteristics,
1). Function will have vertex as (-1, -2) opening downwards.
2). Graph passes through (-3, -3) and (1, -3).
3). Reflection across x-axis.
4). Translation of 2 units down and 1 unit to the left.
5). Horizontal stretch by a factor of 2.
Using translation concepts, it is found that these following transformations happened:
- Reflection across the x-axis.
- Translation of 1 unit left.
- Translation of 2 units down.
The parent function [tex]y = x^2[/tex] points upward and has vertex at (0,0).
- In the graph, the parabola points downward, so it was reflected across the x-axis.
- The x-coordinate of the vertex of the shifted function is -1, thus it was translated 1 unit to left.
- The y-coordinate of the vertex of the shifted function is -2, thus it was translated 2 units down.
A similar problem is given at https://brainly.com/question/4521517