Answer:
Part A: vertex at (-1,4)
Part B: line of symmetry x =-1
Part C: x-intercept x = -3 and x = 1
Part D: y-intercept y = 3
Step-by-step explanation:
Given f(x) = - (x+1)² + 4
The given equation represents a parabola.
The general equation of the parabola with a vertex at (h,k)
f(x) = (x-h)² + k
Part A: To find the vertex, compare the general equation with the given function.
So, the vertex of the function will be at (-1,4)
Part B: the line for the axis of symmetry of function will be at x =-1
Part C: To find x-intercept, put y = 0
So, - (x+1)² + 4 = 0
- (x+1)² = -4
(x+1)² = 4
x + 1 = ±√4 = ±2
x + 1 = 2 OR x + 1 = -2
x = 1 OR x =-3
x-intercept at x = 1 and x = -3
Part D:To find y-intercept, put x = 0
So, y = - (0+1)² + 4 = -1 + 4 = 3
y-intercept at y = 3
See the attached figure.
