In the xy-plane, a line that has the equation y = c for some constant c intersects a parabola at exactly one point . If the parabola has the equation y=-x^ 2 +5x. what is the value of c?

c=6.25

Step-by-step explanation:

If a line that is flat (has a slope of zero) hits only one point of the parabola, it means that point is the vertex of the parabola.

In this case your equation is ---

y= –x^2 + 5x

--- and you just need to write in vertex for the equation:

y=a(x–h)^2 + k

y= –(x–2.5)^2 + 6.25

The vertex is (h,k) or (2.5,6.25)

Since the equation is "y=", k=c

or c=6.25

Thank You.

histogram or dot plot?

step-by-step explanation: