Question

Draw a line for the axis of symmetry of function f. Also mark the x-intercept(s), y-intercept, and vertex of the function. f(x) = -(x + 1)2 + 4

Answer 1

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.

Answer 2

Answer:

Vertex at (-1,4)

Line of symmetry x =-1

x-intercept x = -3 and x = 1

y-intercept y = 3