Mischa wrote the quadratic equation 0 = –x2 + 4x – 7 in standard form
The standard form of quadratic equation is
When y=0 then the standard equation becomes
Now we compare the given equation with
and find the value of a, b,c
-x^2 can be written as -1x^2
a= -1 , b=4 and c=-7
The value of c is -7
Answer: The function is .
Explanation:
It is given that Michael Daniels, is standing on his own 10-yard line. He throws a pass toward the opposite goal line. The football is 2 yards above the ground when the quarterback lets it go.
It follows a parabolic path. Reaching its highest point, 30 yards above the ground. It is caught 50 yards downfield at a point 2 yards above the ground.
So, the initial point is (10,2) and the other point is (60,2).
The height function of a football represents a downward parabola. The maximum point of the function is called vertex. So the vertex is (h,30).
The two point (10,2) and (60,2) have same y-coordinate, therefore the function is maximum at the midpoint of both points.
So, the function is maximum at x=35. Hence the vertex is (35,30)
The standard form of the parabola is,
Where (h,k) is vertex and a is scale factor.
Since vertex is (35,30).
The initial point is (10,2).
So the function of height is.
The graph of the function is shown below.
