Write the equation of the parabola in vertex form.

vertex (0,3), point(-4, -45)

Write the equation of the parabola in vertex form.

vertex (0,3), point(-4, -45)

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

y = ax^{2} + 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 = -3x^{2} + 3

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## Comments

Do you know if the parabola has a vertical axis of symmetry or horizontal axis of symmetry? I am assuming that it is vertical, though it could be horizontal.