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

Respuesta :

unicorn3125

Answer:

              4x² - 1 = 0

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

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