Question 477477
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Hi,
Find the vertex and axis of the parabola y-4=-2(x+3)^2
*Using the vertex form of a parabola, {{{y=a(x-h)^2 +k}}} where(h,k) is the vertex
y-4=-2(x+3)^2 Green
y = -2(x+3)^2 + 4  |vertex (-3,4), line of symmetry is x = -3
 a = -2 < 0, Parabola opens downward, Vertex is a maximum point

parabola having vertex (-2,1) and containing the point (-3,4). 
* y = a(x+2)^2 + 1, 4 = a(-3+2)^2 + 1, a = 3, y = 3(x+2)^2 + 1  Blue
* f(x) = 2x^2 + 12x+7, f(x) = 2(x+3)^2 -11 Purple V(-3,-11) x = -3
* f(x) = 2x^2 + 6x + 5, f(x) = 2(x+3/2)^2 + 1/2, a = 2>0, V(-3/2,{{{highlight(.5)}}})min Yellow
{{{drawing(300,300,  -15,15,-15,15,  blue(line(-3,15,-3,-15))  , grid(1),
circle(-3, 4,0.3),
graph( 300, 300,-15,15,-15,15,0,-2(x+3)^2 + 4,3(x+2)^2 + 1,2(x+3)^2 -11, 2(x+3/2)^2 + 1/2))}}}
 9. Find a quadratic equation with integral coefficients (integers) having roots: {{{-sqrt(5/2)}}},{{{sqrt(5/2)}}}
 (x-5/2)(x+5/2) = 0, x^2 - 25/4 = 0, y = x^2 - 25/4
A rectangular corral is made with a total of 100 feet of fencing on three sides. The fourth side is the side of a barn. 
The greatest possible area for the enclosure would be square: 3s = 100, s = 33 1/3ft