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

Vertex at (-1,4)

Line of symmetry x =-1

x-intercept x = -3 and x = 1

y-intercept y = 3

Answer 2

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

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.