Write the equation of the parabola in vertex form (4,,-2)

Recall that a parabola is the graph representing a quadratic equation, which is standard form is as follows:

    y = ax2 + bx + c  

    where the value of 'a' determines whether the parabola opens upwards of downwards (i.e., the parabola opens upwards if a>0 and opens downwards if a<0) and the axis of symmetry is given by the line x = -b/(2a).

The vertex form of a parabola's (or a quadratic) equations is given by the following formula:

    y = a(x - h)2 + k   ,   where (h, k) is the vertex and the axis of symmetry is given by the line  x = h.

Given that the vertex is at (0, 3), then h = 0   and   k = 3 thus,

    y = a(x - 0)2 + 3

    y = a(x)2 + 3

With a point at (-4, -45), then x = -4   and   y = -45 therefore,

    -45 = a(-4)2 + 3

    -45 = a(16) + 3

Solve for a by first subtracting 3 from both sides of the equation then dividing both sides of the equation by 16:

    -45 - 3 = a(16) + 3 - 3

    -48 = a(16)

    -48/16 = 16a/16

    -3 = a

With a vertex (h, k) at (0, 3) and given that  a = -3, then the equation of this parabola in vertex form is as follows:

    y = a(x - h)2 + k

    y = -3(x - 0)2 + 3

    y = -3x2 + 3

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step-by-step explanation: