SOLUTION: The quadratic function f(x)=ax^2+bx+c has the following characteristics: (i) passes throught the point (2,4); (ii) has a maximum value of 6 when x=4; and (iii) has a zero of x=4

Question 981065: The quadratic function f(x)=ax^2+bx+c has the following characteristics:
(i) passes throught the point (2,4); (ii) has a maximum value of 6 when x=4; and (iii) has a zero of x=4+2√3
Find the values of a,b,c

Thanks a bunch!
Answer by josgarithmetic(39614) (Show Source): You can put this solution on YOUR website!
Vertex is given: (6,4), so you have or .

Using standard form,

but you do not yet know value of a.
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The parabola passes through point (2,4).

substitute the coordinates,

---------one of the values found.

Standard form again:

----------this is general form.
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Compare to the general form,

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The information about the given zero does not play much part in finding the equation for the function:

If z is the other zero, you expect that because the x value for the vertex must be in the middle of the two zeros.

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The two zeros are and .
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