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  a) x = -1, x = 4

  b) y = x^2 -3x -4

Step-by-step explanation:

a) We observe the x-intercepts are x = -1 and x = 4. These are the solutions to y = 0, which is usually what we want in cases like this.

The solutions are x=-1 and x=4.

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b) We know two of the factors are (x +1) and (x -4). There may be an additional constant factor for vertical scaling. One point we can check is the y-intercept.

  y = a(x +1)(x -4)

For x=0, this is ...

  y = a(1)(-4) = -4a

The y-intercept is y = -4, so we have a=1.

The factored equation is ...

  y = (x +1)(x -4)

Multiplying this out gives the equation in standard form:

  y = x^2 -3x -4

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Additional comment

Your teacher may want the standard form equation to be ...

  x^2 -3x -4 = 0

This is the equation of two specific points: x=-1 and x=4. It is not the equation of the graph.