Find the x-intercepts of the parabola with vertex (5,-12) and y-interdept (0,63). Write your answer in this form: (x1,y1), (x2,V2). If necessary, round to the nearest hundredth.

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MrRoyal MrRoyal · Answer 1 · 2022-07-13T20:04:27+02:00

The x-intercepts of the parabola are (3, 0) and (7,0)

The given parameters are:

Vertex (h, k) = (5, -12)

Point (x, y) = (0, 63)

The equation of a parabola is:

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

Substitute (h, k) = (5, -12)

y = a(x - 5)^2 - 12

Substitute (x, y) = (0, 63)

63 = a(0 - 5)^2 - 12

Evaluate

63 = 25a - 12

Add 12 to both sides

25a = 75

Divide by 26

a = 3

Substitute a = 3 in y = a(x - 5)^2 - 12

y = 3(x - 5)^2 - 12

Set y to 0 to determine the x-intercepts

0 = 3(x - 5)^2 - 12

Add 12 to both sides

3(x - 5)^2 = 12

Divide by 3

(x - 5)^2 = 4

Take the square root of both sides

[tex]x - 5 = \pm 2[/tex]

Add 5 to both sides

[tex]x = 5 \pm 2[/tex]

Expand

x = (5 - 2, 5 + 2)

Evaluate

x = (3, 7)

Hence, the x-intercepts of the parabola are (3, 0) and (7,0)