Question

Find the x-intercepts for the parabola defined

by this equation:

y=x2 - 6x + 5

Write your answer as two ordered pairs:

(x1.yı), (x2, y2)

Separate the values with a comma. Round, if

necessary, to the nearest hundredth.

Enter the correct answer.

Answer 1

Explanation:

the x-intercepts are the points, where y=0.

x² - 6x + 5 = 0

with experience I see right away, this is true for x=1 and x=5.

but let's solve this formally.

the general solution to a quadratic excision is

x = (-b ± sqrt(b² - 4ac))/(2a)

in our case

a = 1

b = -6

c = 5

x = (6 ± sqrt((-6)² - 4×1×5))/2 = (6 ± sqrt(36-20))/2 =

= (6 ± sqrt(16))/2 = (6 ± 4)/2 = 3 ± 2

x1 = 3+2 = 5

x2 = 3-2 = 1

so, the 2 x-intercept points are

(1, 0) and (5, 0)