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?

Lightning Apr 20, 2019

#1**+2 **

The curve passes through (0, -13) so -13 = a*0^{2}+b*0+c or c = -13

Hence y = ax^{2} + 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*4^{2} + 4b - 13 to calculate m.

Alan Apr 20, 2019