Question
Determine a quadratic function with this set of characteristics.
x-intercepts of 2 and 7 and maximum value of 25
( How would I find the x-coordinate for the vertex?)
(Thank you!)
x-intercepts of 2 and 7 and maximum value of 25
( How would I find the x-coordinate for the vertex?)
(Thank you!)
Answers
given the x-intercepts,
y = a(x-2)(x-7)
<u>The vertex is midway between the roots</u>, at x = 9/2
y(9/2) = a(5/2)(-5/2) = -25/4 a
Since we want y(9/2) = 25, a = -4
y = -4(x-2)(x-7)
See
http://www.wolframalpha.com/input/?i=-4%28x-2%29%28x-7%29
y = a(x-2)(x-7)
<u>The vertex is midway between the roots</u>, at x = 9/2
y(9/2) = a(5/2)(-5/2) = -25/4 a
Since we want y(9/2) = 25, a = -4
y = -4(x-2)(x-7)
See
http://www.wolframalpha.com/input/?i=-4%28x-2%29%28x-7%29
25 is the maximum value
I used x = 9/2 and I got this equation:
-4(x-4.5)^2+25
I used x = 9/2 and I got this equation:
-4(x-4.5)^2+25
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