✰Answer:
the vertices in order from greatest to least are (0, -253) and (-2, -33).
✰Step-by-step explanation:
The equation for f(x) is f(x) = -4(x-8)^2 + 3.
To find the axis of symmetry, we can use the formula x = -b/2a, where a and b are the coefficients of x^2 and x respectively. In this case, a = -4 and b = 0, so the equation becomes x = -0/(2*(-4)) = 0/(-8) = 0.
Therefore, the axis of symmetry for f(x) is x = 0.
To find the vertex, we can substitute the value of x = 0 into the equation f(x) = -4(x-8)^2 + 3. By simplifying the equation, we get f(0) = -4(0-8)^2 + 3 = -4(-8)^2 + 3 = -4(64) + 3 = -256 + 3 = -253.
So the vertex for f(x) is (0, -253).
Now, let's move on to g(x). The equation for g(x) is g(x) = 3x^2 + 12x + 15.
Since g(x) is in the standard form, we can't use the formula x = -b/2a to find the axis of symmetry directly. However, we can still find the vertex by completing the square.
To complete the square, we need to rewrite g(x) as g(x) = 3(x^2 + 4x) + 15. Now, we can take half of the coefficient of x (which is 4), square it (which is 16), and add it inside the parentheses. This is equivalent to adding and subtracting 16*3 = 48 from the equation.
So g(x) becomes g(x) = 3(x^2 + 4x + 16 - 16) + 15 = 3((x + 2)^2 - 16) + 15 = 3(x + 2)^2 - 48 + 15 = 3(x + 2)^2 - 33.
From this equation, we can see that the vertex is (-2, -33).
To compare the vertices from greatest to least, we have:
1. Vertex of f(x): (0, -253)
2. Vertex of g(x): (-2, -33)
Therefore, the vertices in order from greatest to least are (0, -253) and (-2, -33).
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