Question

Which graph is the graph of f(x)=(x+3(x-2)?

Answer 1

simplify first:
x+3(x-2)
First Outside Inside Last
x^2-2x+3x-6=x^2+x-6

Answer 2

The graph is attached.

Explanation:

This function is in factored form,

f(x) = (x-r₁)(x-r₂), where r₁ and r₂ are the roots of the function. This means the roots, or x-intercepts, of this function are at x = -3 and x = 2.

Next we find the vertex. We start by finding the axis of symmetry; in factored form, this is given by

`x=(r_1+r_1)/(2)`

For our function, we have

x = (-3+2)/2 = -1/2 = -0.5.

We plug this into the function to find the y-coordinate of the vertex:

f(-0.5) = (-0.5+3)(-0.5-2) = 2.5(-2.5) = -6.25

This makes the vertex (-0.5, -6.25).

We plot this vertex; then we plot the roots and draw the parabola through the three points.