SOLUTION: I need help solving the quadratic function,For Each Funtion:(a) determine whether the graph opens down or up, (b) find the axis of symmetry, (c)find the vertex, (d)find the y-inter

Question 214914: I need help solving the quadratic function,For Each Funtion:(a) determine whether the graph opens down or up, (b) find the axis of symmetry, (c)find the vertex, (d)find the y-intercept,(e) find the zeros, and (f) graph the function
the equation is: -x(x-3)

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
I need help solving the quadratic function,For Each Funtion:(a) determine whether the graph opens down or up, (b) find the axis of symmetry, (c)find the vertex, (d)find the y-intercept,(e) find the zeros, and (f) graph the function
the equation is: -x(x-3)
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Equation: y = -x(x-3) = -x^2 + 3x
a = -1; b = 3 ; c = 0
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:(a) determine whether the graph opens down or up,
Answer: Down because a is negative, so as x gets larger
-x^2 gets more negative.
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(b) find the axis of symmetry,
Ans: The equation of the axis of symmetry is x = -b/2a
x = -3/(2*-1) = 3/2
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(c)find the vertex,
Ans: Vertex occurs where x = -b/2a = 3/2
f(x) = -x^2 + 3x
Find the y-value: f(3/2) = -(3/2)^2+3(3/2)
f(3/2) = -(9/4)+9/2 = -9/4 + 18/4 = 9/4
So the vertex is (3/2 , 9/4)
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(d)find the y-intercept,
y = -x^2+3x
To find the y-intercept let x=0.
Then y = -0^2+3*0 = 0+0 = 0
So the y-intercept is (0,0) or simply zero.
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(e) find the zeros,
Let y = 0 and solve for "x":
-x^2+3x = 0
Factor:
-x(x-3)=0
-x = 0 or x-3 = 0
x = 0 or x = 3
Those are the zeroes.
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(f) graph the function
Need to plot several points by giving a value for "x"
and finding the y-value associated with that x-value.
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Cheers,
Stan H.
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