NEED ASAP!!! MATH PROBLEM

Question

Write the function f(x) = x^2 - 6x - 16 in a form that would make it easier to graph and explain why this form is easy to graph and how you a graph the function in this form.

Answer 1

First, f(x) can be written as a y, so y=x²-6x-16

Next, you can have two options here: 1) change this equation into the vertex form of a parabola or 2) find the coordinate for the vertex.

1) The first option is more detailed - The vertex form of a parabola is: y=(x-h)²+k where the (h,k) is the vertex of the parabola.

We will have to use “completing the square” method to transform the equation from the general form to the vertex form.

y+16+9 = x²-6x+9

y+25 = (x-3)²

y=(x-3)²-25, so the vertex is (3, -25)

2) The second option uses the coordinate (-b/2a, f(-b/2a)), where ax²+bx+c is your equation in standard form.

So, a=1 and b=-6 therefore, (3, f(3)) yields a vertex at (3, -25)

Answer 2

Standard form for quadratics can be tricky to graph, since it doesn't give you information about where the function intersects the x-axis just at a glance.

As such, you can change the function into factored form, which tells you where its roots are:

f(x) = (x + 2)(x - 8)

This form makes graphing easier, as you can immediately tell that it has roots at x = -2 and x = 8, and by plugging 0 in, that it intersects the y-axis at y = -16. In other words, factored form just gives more information at a glance.