Hello!
The answer is:
The quadratic function that fits the given picture is:
[tex]y=-3x^{2}+13x-5[/tex]
Why?
We can solve the problem and find the correct function that fits the curve below by finding which function intercepts the y-axis at -5 (we can see it from the picture), also, we need to look for a function that represents a parabola opening upwards. We need to remember that when a parabola is opening upwards, its quadratic term coefficient is negative.
So, we can see that from the given functions, the only function that represents a parabola opening upwards and its y-intercept is located at y equal to -5 is the second option:
[tex]y=-3x^{2}+13x-5[/tex]
We have that :
[tex]a=-3(negative)\\b=13\\c=-5(y-intercept)[/tex]
We can see that the quadratic term (a) is negative, and the quadratic function intercepts the y-axis at y equal to -5.
Hence, the answer is:
The quadratic function that fits the given picture is:
[tex]y=-3x^{2}+13x-5[/tex]
Have a nice day!
Note: I have attached a picture for better understanding.
