Given: y = (x + 1 )^2 - 4
This is an equation of a parabola in vertex form:
y = a(x - h)^2 + k; " where the vertex is " (h, k) and
the axis of symmetry is x = h and a is a constant.
Find the vertex and axis of symmetry:
vertex: (-1, -4); " axis of symmetry: "x = -1
Find the y-intercept by setting x = 0:
y = (0+1)^2 - 4 = 1-4 = -3 => (0, -3)
Find x-intercepts by setting y = 0 and factoring or using the quadratic formula or completing the square:
0 = (x + 1 )^2 - 4 = (x^2 + 2x + 1) - 4
x^2 + 2x -3 = (x - 1)(x + 3) = 0
x-intercepts: (-3, 0), (1, 0)
To graph, plot the intercepts and the vertex. You can use the technique of point-plotting to add additional points.
Since x is an independent variable, you can select different x values and calculate the corresponding y values.
ul(" "x" "|-4" "|-2" "|" "2" "|)
" "y" "|" "5" "|-3" "|" "5" "|
graph{(x + 1 )^2 - 4 [-10, 10, -5, 5]}
