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Question 674319: For each equation, identify the equation of the axis of symmetry, the coordinates of the vertex, the y-intercept, the zeros, and the maximum or minimum values.
y = x2 + 4x + 3
y = -2(x - 3)2 + 9
y = 3(x - 0.5)2
Help please?
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! For each equation, identify the equation of the axis of symmetry, the coordinates of the vertex, the y-intercept, the zeros, and the maximum or minimum values.
y = x2 + 4x + 3
y = -2(x - 3)2 + 9
y = 3(x - 0.5)2
**
All 3 given equations are parabolas and take the standard form: y=A(x-h)^2+k, (h,k)=(x,y) coordinates of the vertex. A is a coefficient that affects the width of the curve. If A>0, parabola opens upwards and parabola has a minimum. If A<0, parabola opens downwards and parabola has a maximum.
..
y = x^2 + 4x + 3
complete the square
y = (x^2+4x+4)+3-4
y = (x+2)^2-1
vertex: (-2,-1)
axis of symmetry: x=-2
minimum: -1
..
y-intercept
set x=0
y=3 (from original equation)
..
x-intercepts (zeros)
set y=0
(x+2)^2-1=0
(x+2)^2=1
x+2=±√1=±1
x=-2±1
x=-3 and -1
..
I will let you do the remaining 2 equations
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