How do I find the quadratic equation with the following: passing through (1/2,0), (-1/2,0), and (0,1) ??

Step-by-step explanation:

passing through (¹/₂,0) and (-¹/₂,0) so:  ¹/₂ and -¹/₂ are roots of the equation

so:

     y = a(x - ¹/₂)(x-(-¹/₂))

     y = a(x - ¹/₂)(x +¹/₂)

     y = a(x² - ¹/₄)

and passing through (0,1) so:

     1 = a(0² - ¹/₄)

     1 = - ¹/₄a

     a = -4

therefore:

                 y = 4(x² - ¹/₄)

                 y = 4x² - 1

So the quadratic equation:   4x² - 1 = 0

34.5 cm

step-by-step explanation:

generally for a circular segment of angle, θ° and radius r

arc length

= (θ/360) x circumference

= (θ/360) x 2πr

in our case, θ = 60°, π=3.142 and r = 33 cm

substitute into above formula

arc length

= (60/360) x 2(3.142)( 33) = 34.5 cm