SOLUTION: Hello, need an explanation on how to find the x intercepts, and the vertex of this equation y is less than or equal to -x^2+3x+2. I do not know how to factor yet, so if we could do

Algebra ->  Algebra  -> Quadratic Equations and Parabolas -> SOLUTION: Hello, need an explanation on how to find the x intercepts, and the vertex of this equation y is less than or equal to -x^2+3x+2. I do not know how to factor yet, so if we could do      Log On

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Question 423208: Hello, need an explanation on how to find the x intercepts, and the vertex of this equation y is less than or equal to -x^2+3x+2. I do not know how to factor yet, so if we could do it by guessing two points and checking by plugging them into the equation and finding some easy to graph points. Thanks soOoOoOo much!
Answer by stanbon(57400) About Me  (Show Source):
You can put this solution on YOUR website!
need an explanation on how to find the x intercepts, and the vertex of this equation y is less than or equal to -x^2+3x+2.
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a = -1 ; b = 3 ; c = 2
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Vertex occurs at x = -b/(2a) = -3/(-2) = 3/2
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Vertex y-value: f(3/2) = -(3/2)^2+3(3/2)+2 = -9/4+(9/2)+2 = 17/4
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Vertex:(3/2 , 17/4)
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x-intercepts:
solve -x^2+3x+2 = 0
x = [-3 +- sqrt(9-4*-1*2)]/(-2)
= [-3 +- sqrt(17)]/(-2)
Those are the x-intercepts
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Cheers,
Stan H.
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