Question

Find the x-intercept of the parabola of with vertex (1,20) and the y-intercept (0,16). write your answer in this form: (x1,y1),(x2,y2)

Answer 1

I assume that the parabola in this particular problem is one whose axis of symmetry is parallel to the y axis. The formula we're going to use in this case is (x-h)2=4p(y-k). We know variables h and k from the vertex (1,20) but p is not given. However, we can solve for p by substituting values x and y in the formula with the y-intercept:

(0-1)^2=4p(16-20)

Solving for p, p=-1/16.

Going back to the formula, we can finally solve for the x-intercepts. Simply fill in variables p, h and k then set y to zero:

(x-1)^2=4(-1/16)(0-20)
(x-1)^2=5
x-1=(+-)sqrt(5)
x=(+-)sqrt(5)+1

Here, we have two values of x

x=sqrt(5)+1 and
x=-sqrt(5)+1

thus, the answers are: (sqrt(5)+1,0) and (-sqrt(5)+1,0).