write the vertex form of a parabola that satisfies the conditions given. Then write the equation in the form y=a^+bx+c. vertex (-3,-4) and a=5.
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To find the vertex form of a parabola that satisfies the given conditions, we can start with the general form of the equation of a parabola, which is y = a(x - h)^2 + k, where (h, k) represents the vertex.
Given that the vertex is (-3, -4) and a = 5, we can substitute these values into the vertex form equation:
y = 5(x - (-3))^2 + (-4)
Simplifying this expression, we have:
y = 5(x + 3)^2 - 4
Now, let's expand and rewrite in the standard form, y = ax^2 + bx + c:
y = 5(x^2 + 6x + 9) - 4
y = 5x^2 + 30x + 45 - 4
y = 5x^2 + 30x + 41
So, the equation of the parabola in the form y = ax^2 + bx + c, given the vertex (-3, -4) and a = 5, is y = 5x^2 + 30x + 41.