SOLUTION: What are the x-intercepts of a parabola witha vertex (4,-1) and y intercept of (0,15) with answer in the form (x1,y1), (x2,y2)

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: What are the x-intercepts of a parabola witha vertex (4,-1) and y intercept of (0,15) with answer in the form (x1,y1), (x2,y2)      Log On


   

Question 749467: What are the x-intercepts of a parabola witha vertex (4,-1) and y intercept of (0,15) with answer in the form (x1,y1), (x2,y2)
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
Checking how the vertex and the y intercept are arranged on a graph, we can understand that the parabola opens upward, having the vertex as a minimum.

y=a%28x-h%29%5E2%2Bk standard form in which a%3E0.
Using your vertex coordinates,
y=a%28x-4%29%5E2-1

The given y intercept point allows the equation, 15=a%280-4%29%5E2-1
15=a%2A16-1
16=a%2A16
a=1

Standard form equation is then specifically y=1%2A%28x-4%29%5E2-1
or simply
highlight%28y=%28x-4%29%5E2-1%29

From that standard form equation, you can finish finding the x intercepts on your own. Just let y = 0 and solve for x. %28x-4%29%5E2-1=0.