Find the x-intercepts of the parabola with vertex (4,75) and y-intercept (0,27). write your answer in this form: (x1,y1), (x2,72). if necessary, round to the nearest hundredth.

(- 1, 0), (9, 0)

Step-by-step explanation:

The equation of a parabola in vertex form is

y = a(x - h)² + k

where (h, k) are the coordinates of the vertex and a is a multiplier

here (h, k) = (4, 75), so

y = a(x - 4)² + 75

To find a substitute (0, 27) into the equation

27 = a(- 4)² + 75 , that is

27 = 16a + 75 ( subtract 75 from both sides )

16a = - 48 ( divide both sides by 16 )

a = - 3, thus

y = - 3(x - 4)² + 75 ← equation in vertex form

To obtain the x- intercepts let y = 0

- 3(x - 4)² + 75 = 0 ( subtract 75 from both sides )

- 3(x - 4)² = - 75 ( divide both sides by - 3 )

(x - 4)² = 25 ( take the square root of both sides )

x - 4 = ± = ± 5

Add 4 to both sides

x = 4 ± 5, hence

x = 4 - 5 = - 1 or x = 4 + 5 = 9

Substitute these values into the equation for corresponding values of y

x = - 1 : y = - 3(- 5)² + 75 = - 75 + 75 = 0 → (- 1, 0)

x = 9 : y = - 3(5)² + 75 = = 75 + 75 = 0 → (9, 0)

The x- intercepts are (- 1, 0), (9, 0)

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