Question

Let ​ f(x)=x2−6x−27 ​ . Enter the x-intercepts of the quadratic function in the boxes. x = and x =

Answer 1

-3, 9

Explanation:

x^2 -6x - 27=

= x^2 - 9x + 3x - 27

= x(x - 9) + 3(x - 9)

= (x + 3)(x - 9)

x = -3, x = 9

Answer 2

x = 9

x = - 3

Explanation:

This factors.

The best way to do this is to start by seeing what answers are possible. Start with 27. What 2 numbers multiply to 27. There aren't many.

27: 1 * 27

27: 3*9

Now you need the two numbers to add to -6. That means the larger one should be -

The answer is 3 and 9

So the factors are

(x - 9)(x + 3)

x - 9 = 0

x = 9

========

x + 3 = 0

x = - 3

================

The intercepts are the points (9,0) and (-3,0)

x = 9

x = - 3