Question

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

Answer 1

4x² - 1 = 0

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