9514 1404 393
Answer:
vertex: (2, -3.2)
axis of symmetry: x = 2
zeros: x=0, x=4
formula for axis of symmetry:
- x = <x-coordinate of vertex>
- x = -b/(2a) . . . . . . . where the quadratic is ax^2 +bx +c
- x = average of zeros, (z1 +z2)/2
Step-by-step explanation:
a) The vertex x-coordinate is halfway between the zeros, so is x = (0+4)/2 = 2. It is where the graph has a turning point.
The vertex y-coordinate is the low point of this graph. It is not on a grid line, so we can only guess at its value. I choose to call it -3.2.
The vertex is (2, -3.2).
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b) The axis of symmetry is the vertical line through the vertex. The constant in its equation is the x-coordinate of the vertex:
x = 2
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c) The zeros of the function are where the function crosses the x-axis. These are marked on the graph with red dots. The zeros are x=0 and x=4.
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d) When the quadratic is written in standard form, ax^2 +bx +c, the equation of the axis of symmetry is ...
x = -b/(2a) . . . . . perhaps this is the formula you're being asked for (?)
When there is no equation, the axis of symmetry can be found from the graph a couple of ways. One is to identify the x-coordinate of the vertex.
x = <x-coordinate of the vertex>
Another is to average the zeros, since they are symmetrical about the axis of symmetry.
x = average of zeros = (z1 +z2)/2
If the quadratic is written in vertex form, the vertex coordinate is the constant in the equation for the axis of symmetry.
y = a(x -h)^2 +k . . . . . quadratic with vertex (h, k)
x = h . . . . . . equation of axis of symmetry
where h and k are the center and x and y are the coordinates you're given. We need to solve for the radius to finish this off correctly. Filling in, we have 
and 
, giving us that 
. Therefore, our equation is 