for the equation ( y = -3x^{2}+12x - 7 ), what is the maximum value of ( y )?
for the equation ( y = -3x^{2}+12x - 7 ), what is the maximum value of ( y )?
Answer
Explanation:
Step1: Find the x - coordinate of the vertex
For a quadratic function (y = ax^{2}+bx + c), the x - coordinate of the vertex is given by (x=-\frac{b}{2a}). Here, (a=-3) and (b = 12). (x=-\frac{12}{2\times(-3)}=\frac{-12}{-6} = 2)
Step2: Substitute x into the function to find y
Substitute (x = 2) into (y=-3x^{2}+12x - 7). (y=-3\times(2)^{2}+12\times2-7) (y=-3\times4 + 24-7) (y=-12 + 24-7) (y=12-7) (y = 5)
Answer:
(y = 5)