Question

Write an equation for the quadratic graphed below: x-intercepts: (-1,0) and (4,0); y-intercept: (0,1)

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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