find the x-intercepts of the parabola with vertex(-1,-16)and the y-intercept(0,-15)

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find the x-intercepts of the parabola with vertex(-1,-16)and the y-intercept(0,-15).write your answer in this form:(x1,y1)(x2,y2).

Apr 29th, 2015

Vertex = (-1, -16)

y-intercept = (0, -15)


Equation of the parabola in vertex form is

y = a(x-h)^2 + k

where (h, k) is the vertex of the parabola.

So, (h, k) = (-1, -16)


So, equation of the parabola becomes

y = a(x - (-1))^2 + (-16)

y = a(x + 1)^2 - 16


Since (0, -15) is the y-intercept, it must satisfy the above equation

So,

-15 = a(0 + 1)^2 - 16

-15 + 16 = a(1)^2

a = 1


So equation of the parabola is

y = 1(x + 1)^2 - 16

y = (x + 1)^2 - 16


To find the x intercepts, put  y = 0

 (x + 1)^2 - 16 = 0

 (x + 1)^2 = 16

x + 1 =  √16

x + 1 = ± 4

x + 1 = 4     or        x + 1 = -4

x = 4 - 1      or        x = -4 - 1

x = 3           or        x = -5

  

So the x-intercepts are  (3, 0)  and (-5, 0).



Apr 29th, 2015

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