Question 389589
Find the X-intercept of the parabola with vertex (-1,-108) and y-intercept of (0,-105).
<pre>
Use the form for the parabola:

y = a(x - h)² + k with vertex (h,k) = (-1,-108)

y = a[x - (-1)]² + (-108) 
y = a(x + 1)² - 108

Since y-intercept (0,-105) must satisfy the equation
we substitute 0 for x any -105 for y:

   y = a(x + 1)² - 108
-105 = a(0 + 1)² - 108
-105 = a(1)² - 108
-105 = a*1 - 108
-105 = a - 108
   3 = a

So we substitute 3 for a in

y = a(x + 1)² - 108

and get

y = 3(x + 1)² - 108

That's the equation of the parabola

To find the x intercept we substitute 0 for y:

  0 = 3(x + 1)² - 108
108 = 3(x + 1)²

Divide both side by 3

 36 = (x + 1)²

Use the principle of square roots:
  __
{{{""+- sqrt("")}}}36 = x + 1

  ±6 = x + 1

Using the +6

   6 = x + 1
   5 = x

Using the -6

  -6 = x + 1
  -7 = x

So there are two x-intercepts (5,0) and (-7,0)

{{{graph(500,500,-10,10,-150,150,3(x+1)(x+1) - 108)}}}

Edwin</pre>