Answer:
x intercept: (3, 0), (7, 0)
y-intercept: (0, -21)
vertex : (5,4)
the graph points down
Step-by-step explanation:
f(x) = - (x - 3)(x - 7)
f(x) = - (x^2 - 7x - 3x + 21)
f(x) = - (x^2 - 10x + 21)
f(x) = -x^2 + 10x - 21
x-intercept when f(x) = 0 so
x - 3 = 0; x = 3
x - 7 = 0; x = 7
x intercept: (3, 0), (7, 0)
y-intercept when x = 0 so y = -21
y-intercept: (0, -21)
vertex:
x = -b/2a
x = -10/ 2(-1)
x = 5
plug in x = 5 into the equation to find y
y = -(5)^2 + 10(5) - 21
y = -25 + 50 - 21
y = 4
so vertex : (5,4)
Since a = - 1<0, the graph is going downward and has maximum
