SOLUTION: y = (-4x^2) - 12x + 9 a. Determine the vertex of the function b. determine if the funtion is concave up or down c. Determine the zeros if any

Algebra ->  Rational-functions -> SOLUTION: y = (-4x^2) - 12x + 9 a. Determine the vertex of the function b. determine if the funtion is concave up or down c. Determine the zeros if any      Log On


   

Question 318058: y = (-4x^2) - 12x + 9
a. Determine the vertex of the function
b. determine if the funtion is concave up or down
c. Determine the zeros if any
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
y = (-4x^2) - 12x + 9
Complete the square and put the eqaution in vertex form, y=a%28x-h%29%5E2%2Bk
where (h,k) is the vertex.
y=+-4x%5E2-12x%2B9+
y=-4%28x%5E2%2B3x%29%2B9
y=-4%28x%5E2%2B3x%2B9%2F4%29%2B9%2B4%289%2F4%29
y=-4%28x%2B3%2F2%29%5E2%2B18
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a)The vertex is (-3%2F2,18).
b) The parabola opens downward since the coefficient for x%5E2 is negative.
c) Since the vertex occurs at y=18 and it opens downwards, the curve will cross the x-axis.
y=-4%28x%2B3%2F2%29%5E2%2B18=0
4%28x%2B3%2F2%29%5E2=18
%28x%2B3%2F2%29%5E2=18%2F4
x%2B3%2F2=0+%2B-+%283%2F2%29sqrt%282%29
highlight%28x=-3%2F2+%2B-+%283%2F2%29sqrt%282%29%29
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