How do you use the important points to sketch the graph of f(x) = -x^2 + 14x - 48?

1 Answer
Apr 15, 2017

graph{-x^2 + 14x - 48 [-18.18, 27.43, -16.63, 6.17]}

Explanation:

Find maximum point or vertex:

max(ax^2 + bx + c) = ((-b)/(2a), f((-b)/(2a)))

In this case: b = 14, a = -1

max(-x^2 + 14x - 48) = ((-14)/(-2), f((-14)/(-2)))
max(-x^2 + 14x - 48) = (7, f(7))
max(-x^2 + 14x - 48) = (7, 1)

Now let's see if it opens up or downwards. As a < 0, it opens downwards.

Now let's see where it cuts both the x axis (y = 0) and the y axis (x = 0).

x-axis (y = 0): -x^2 + 14x - 48=0 => x = 6,8
y-axis (x = 0): 0 + 0 - 48 => y = -48

Plot the max point (7,1), the two points on the x-axis the parabola intersects (6,0) " and " (8,0), the point in the y axis it intersects (0,-48), and join them together smoothly .

Ta-da!