Step-by-step explanation:
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
