SOLUTION: Find the x intercepts of the parabola with vertex (1,-13) and y-intercept (0,-11). Write your answer i’m this form: (x1y1),(x2,y2). If necessary, round to the nearest hundredth.

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: Find the x intercepts of the parabola with vertex (1,-13) and y-intercept (0,-11). Write your answer i’m this form: (x1y1),(x2,y2). If necessary, round to the nearest hundredth.      Log On


   



Question 1163354: Find the x intercepts of the parabola with vertex (1,-13) and y-intercept (0,-11). Write your answer i’m this form: (x1y1),(x2,y2). If necessary, round to the nearest hundredth.
Answer by greenestamps(13203) About Me  (Show Source):
You can put this solution on YOUR website!


With vertex (1,-13), the vertex form of the equation is

%28y%2B13%29+=+a%28x-1%29%5E2

Use the given point (0,-11) to determine the coefficient a:

-11%2B13+=+a%28-1%29%5E2
2+=+a

The equation in vertex form is

%28y%2B13%29+=+2%28x-1%29%5E2

To find the x-intercepts, set y=0 and solve

13+=+2%28x-1%29%5E2
%28x-1%29%5E2+=+13%2F2
x+=+1%2B-sqrt%2813%2F2%29

You can write those roots in the requested form....

A graph, to let you see if your answers are reasonable....

graph%28400%2C400%2C-5%2C5%2C-15%2C5%2C2%28x-1%29%5E2-13%29