Question

Graph the function f (x) = (x+3)(x +

5).
Use the parabola tool by plotting the vertex and then another point on the parabola.

Answer 1

see attached

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)