The parabola with the minimum at (4, -3) is the third option:
![y = 0.5*x^2 - 4x + 5](https://tex.z-dn.net/?f=y%20%3D%200.5%2Ax%5E2%20-%204x%20%2B%205)
<h3>
Which of the given parabolas has a minimum at (4, -3)?</h3>
Remember that for a parabola of the form:
![y = a*x^2 + b*x + c](https://tex.z-dn.net/?f=y%20%3D%20a%2Ax%5E2%20%2B%20b%2Ax%20%2B%20c)
If a > 0, the minimum is at the x-value of the vertex:
![x = \frac{-b}{2a}](https://tex.z-dn.net/?f=x%20%3D%20%5Cfrac%7B-b%7D%7B2a%7D)
If a < 0, there is no minimum (so we discard option 2).
Taking the third option:
![y = 0.5*x^2 - 4x + 5](https://tex.z-dn.net/?f=y%20%3D%200.5%2Ax%5E2%20-%204x%20%2B%205)
The x-value of the vertex is:
![x = \frac{-(-4)}{2*0.5} = 4](https://tex.z-dn.net/?f=x%20%3D%20%5Cfrac%7B-%28-4%29%7D%7B2%2A0.5%7D%20%3D%204)
As expected.
To get the y-value of the vertex (and minimum) we just evaluate the parabola equation in x = 4.
![y = 0.5*(4)^2 - 4*4 + 5 = -3](https://tex.z-dn.net/?f=y%20%3D%200.5%2A%284%29%5E2%20-%204%2A4%20%2B%205%20%3D%20-3)
So the minimum is at (4, -3), as expected, so that is the correct option.
If you want to learn more about parabolas:
brainly.com/question/4061870
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