Final answer:
To find the value of c, we need to determine the point at which the line 2y = c intersects the parabola y = -2x² + 9x.
Step-by-step explanation:
To find the value of c, we need to determine the point at which the line 2y = c intersects the parabola y = -2x² + 9x. Substitute the equation of the line into the equation of the parabola:
2y = c
-2x² + 9x = c
Rearrange the equation to get:
2x² - 9x + c = 0
Since the line intersects the parabola at exactly one point, the quadratic equation should have exactly one solution. For a quadratic equation to have one solution, the discriminant (b² - 4ac) must equal zero. Plugging in the values:
(-9)² - 4(2)(c) = 0
Solving this equation will give us the value of c.