SOLUTION: Find the x-intercepts of the parabola with vertex (-3,-14) and y-intercept (0,13). Write your answer in this form: (x1,y1) (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 (-3,-14) and y-intercept (0,13). Write your answer in this form: (x1,y1) (x2,y2). If necessary round to the nearest hundredth.      Log On


   

Question 742539: Find the x-intercepts of the parabola with vertex (-3,-14) and y-intercept (0,13). Write your answer in this form: (x1,y1) (x2,y2). If necessary round to the nearest hundredth.
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
Use standard form equation to fill-in the vertex information from your given (h, k). y=a%2A%28x%2B3%29%5E2-14, and we know before continuing that a%3E0, as we can find inspecting the vertex and the y intercept.

Substitute the y-intercept coordinate values into the equation and solve for a.
13=a%280%2B3%29%5E2-14
13%2B14=9%2Aa
27=9%2Aa
a=3

Equation for this parabola is highlight%28y=3%28x%2B3%29%5E2-14%29.

Finding the x-intercepts requires just setting y=0 and solve for x from the standard form equation just found:
3%28x%2B3%29%5E3-14=0
3%28x%2B3%29%5E3=14
%28x%2B3%29%5E2=14%2F3
x%2B3=0%2B-+sqrt%2814%2F3%29
highlight%28x=-3%2B-+sqrt%2814%2F3%29%29, the x-intercepts.