1000 m = 1 km
5000 m = 5 km
They have traveled 5 km so far.
Subtract what they traveled from total distance:
24-5 = 19 km left.
y = 3/2x + b
Plug in the point (2,2) and solve for b.
2 = (3/2)(2) + b
2 = 3 + b
b = -1
Final equation is y = 3/2x - 1.
So you would plug in 0 for a from the beginning since this is numerical slope definition of a derivative
Answer
y = 1(x +1) - 3
Explanation
A quadratic equation of the form y = ax^2 + bx + c
This written in complete the square form provides you with the vertex (either a maximum or minimum point depending on the equation).
This results in y = a(x + p) + q
Where - p is the x value and q is the y value of turning point.
For graph 22, x = -1 and y = -3
Therefore, the equation is of the form
y = a(x + 1) - 3 (*)
We still need the value a, this can be obtained by using the y-intercept we are given.
We are told x = 0 when y = -2
Substitute this in (*) equation:
-2 = a(0+1) - 3
-2 = a - 3
a = 1
Therefore final equation is
y = 1(x +1) - 3
This should provide you with the train of thought of how the second question should also be tackled.
If unsure about why the equation
y = a(x + p) + q gives the vertex ask in comments I will respond
3h - 8h + 10 = 10 - 5h
-5h + 10 = 10 - 5h
infinitely many solutions
