Answer:
see attached
Step-by-step explanation:
You want to graph the function f(x) = (x +3)(x +5).
Zeros
The x-intercepts of the parabola are the values of x where the factors are zero:
x +3 = 0 ⇒ x = -3 . . . . . . point (-3, 0)
x +5 = 0 ⇒ x = -5 . . . . . . point (-5, 0)
Vertex
The vertex is on the line of symmetry, halfway between these x-intercept:
x-coordinate = (-3 +(-5))/2 = -4
y-coordinate = f(-4) = (-4 +3)(-4 +5) = (-1)(1) = -1
The vertex is (-4, -1).
Now, you have the vertex and two other points on the curve. You can use these with your parabola tool to graph the function.
vertex: (-4, -1)
other point: (-3, 0) or (-5, 0)
