can you help me with pre-cal homework?
Find B so that F(x)=-x^2+bx-75 has a maximum value of 25.
help pliz i dont get it :(
- mathboyLv 6hace 9 añosRespuesta favorita
For y = ax² + bx + c there is a turning point corresponding to
x = -b / 2a
In the example given we know it is a maximum turning point since coefficient of x² is negative which gives a downward opening parabola.
In this case max value attained when x = -b/-2 = b/2.
f(b/2) = -(b/2)² + b(b/2) - 75 = 25
= -b²/4 + b²/2 - 75 = 25
b² / 4 - 75 = 25
b² = 400
b= -20 and b = 20
When b = -20 roots are x = -15 , -5
When b = 20 roots are 5 , 15