Question

Please help me. give 10 points


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Answer 1

x intercept: (3, 0), (7, 0)

y-intercept: (0, -21)

vertex : (5,4)

the graph points down

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