How do you find the vertex and the intercepts for y= (x-4) (x+2)?

1 Answer
Jun 26, 2018

See below

Explanation:

For the vertex, we need to get our equation in standard form. Using FOIL, it can be rewritten as y=x^2-2x-8. To find its x-coordinate, use the formula x=-b/(2a):

x=(-(-2))/(2(1))=2/2=1

The y-coordinate is found by plugging our answer back into the equation:

y=(1)^2-2(1)-8
y=1-2-8=-7

Vertex: (1,-7)

By "intercepts", I believe you mean both the x-intercepts and the y-intercept. For the x-intercepts, we can use the factored equation, set y to 0, and solve:

0=(x-4)(x+2)
x-4=0
x=4
x+2=0
x=-2

X-intercepts: (4,0), (-2,0)

To find the y-intercept, we will use the standard form of our equation, set x to 0, and solve:

y=0^2-2(0)-8
y=-8

Y-intercept: (0,-8)

Hope this helped!