Answer:
![y = \frac{1}{2}x^{2} - 3x + 11.5](https://tex.z-dn.net/?f=y%20%3D%20%5Cfrac%7B1%7D%7B2%7Dx%5E%7B2%7D%20-%203x%20%2B%2011.5)
Step-by-step explanation:
Vertex form of a quadratic equation;
![y = a( x - h )^{2} + k](https://tex.z-dn.net/?f=y%20%3D%20a%28%20x%20-%20h%20%29%5E%7B2%7D%20%2B%20k)
Vertex of the parabolas (h, k)
The vertex of the parabola is either the minimum or maximum of the parabola. The axis of symmetry goes through the x-coordinate of the vertex, hence h = -3. The minimum of the parabola is the y-coordinate of the vertex, so k= 7. Now substitute it into the formula;
![y = a ( x + 3 ) ^{2} + 7](https://tex.z-dn.net/?f=y%20%3D%20a%20%28%20x%20%2B%203%20%29%20%5E%7B2%7D%20%2B%207)
Now substitute in the given point; ( -1, 9) and solve for a;
![9 = a( (-1 ) + 3)^2 + 7\\9 = a (2)^{2} + 7\\9 = 4a + 7\\-7 -7\\2 = 4a\\\frac{1}{2} = a\\](https://tex.z-dn.net/?f=9%20%3D%20a%28%20%28-1%20%29%20%2B%203%29%5E2%20%2B%207%5C%5C9%20%3D%20a%20%282%29%5E%7B2%7D%20%2B%207%5C%5C9%20%3D%204a%20%2B%207%5C%5C-7%20%20%20%20%20%20%20%20%20%20%20-7%5C%5C2%20%3D%204a%5C%5C%5Cfrac%7B1%7D%7B2%7D%20%3D%20a%5C%5C)
Hence the equation in vertex form is;
![y = \frac{1}{2}(x - 3)^{2} + 7](https://tex.z-dn.net/?f=y%20%3D%20%5Cfrac%7B1%7D%7B2%7D%28x%20-%203%29%5E%7B2%7D%20%2B%207)
In standard form it is;
![y = \frac{1}{2}x^{2} - 3x + 11.5](https://tex.z-dn.net/?f=y%20%3D%20%5Cfrac%7B1%7D%7B2%7Dx%5E%7B2%7D%20-%203x%20%2B%2011.5)
$365 increased to $428
365/428=1.17
which translates to an 117% increase
The identity property of addition states that any number plus zero equals the original number. So, 6 + 0 = 6 shows the identity property of addition. Other number sentences that show this property would include: 8 + 0 = 8, 153 + 0 = 153, and 1,899,888 + 0 = 1,899,888. In each case, the original number plus 0 equals the original number. It doesn't matter how large or small the original number is.
<span>37x^3y^6 and x^6y^2
</span>greatest common factor: x^3y^2