Question

Let ƒ(x) = −x^2+6x−8. Find the vertex and x− and y−intercepts of the graph of ƒ.

Answer 1

Let's factor it.

-x^2+6x-8
-(x^2-6x+8)
-(x-4)(x-2)

That means (x-4) is a factor and (x-2) is a factor. If it's a factor, then it's equal to 0.

x-4=0
x=4

x-2=0
x=2

Your roots/zeros/x-intercepts (all are interchangeable terms) are 2 and 4.


For the y-intercept, you have to look at the equation itself. The constant term (the one with no variable attached) is the value of the y-intercept, so it's -8.

Answer 2

Nice explanation, @tomhue . I would, however, re-write your statement, "If it's a factor, then it's equal to zero" as: "We now set each of these two possible factors = to zero separately and solve the resulting equations for x. Each such x is the x-coordinate of one of the x-intercepts."