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The graph of the quadratic y = ax^2 + bx + c has the following properties: (1) The maximum value of y = ax^2 + bx + c is 5, which occurs at x = 3. (2) The graph passes through the point (0,-13). If the graph passes through the point (4,m), then what is the value of m?

 Apr 20, 2019
 #1
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The curve passes through (0, -13) so -13 = a*02+b*0+c or c = -13

 

Hence y = ax2 + bx -13

 

Maximum occurs when  y = 5 and x = 3, so 5 = 9a + 3b -13

or 9a + 3b = 18, or 3a + b = 6 ...(1)

 

The slope is given by slope = 2ax + b, and this must be zero at a maximum,

so 2a*3 + b = 0 or 6a + b = 0 ...(2)

 

You can use equations (1) and (2) to find a and b, then use

m = a*42 + 4b - 13 to calculate m.

 Apr 20, 2019

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