Answers

1. Answer:

   y = (1/4)x² – (5/4)x + 1

   Step-by-step explanation:

   The x-intercepts of the quadratic equation are simply it’s roots.

   Thus, we have;

   (x + 1) = 0 and (x – 4) = 0

   Now, formula for quadratic equation is;

   y = ax² + bx + c

   Where c is the y intercept.

   At y-intercept: (0,1), we have;

   At (-1,0), thus;

   0 = a(1²) + b(1) + 1

   a + b = -1 – – – (1)

   At (4,0), thus;

   0 = a(4²) + b(4) + 1

   16a + 4b = -1

   Divide both sides by 4 to get;

   4a + b = -1/4 – – – (2)

   From eq 1, b = -1 – a

   Thus;

   4a + (-1 – a) = -1/4

   4a – 1 – a = -1/4

   3a – 1 = -1/4

   3a = 1 – 1/4

   3a = 3/4

   a = 1/4

   b = -1 – 1/4

   b = -5/4

   Thus;

   y = (1/4)x² – (5/4)x + 1

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