Question

given the quadratic function $f(x) = -4x^2 + 8x - 1$, what is the maximum value?
a. 4
b. -1
c. 3
d. 2

Explanation:

Step1: Find the x - coordinate of the vertex

For a quadratic function \( f(x)=ax^{2}+bx + c \), the x - coordinate of the vertex is given by \( x =-\frac{b}{2a} \). In the function \( f(x)=- 4x^{2}+8x - 1 \), \( a=-4 \), \( b = 8 \), and \( c=-1 \).
So, \( x=-\frac{8}{2\times(-4)}=-\frac{8}{-8} = 1 \).

Step2: Find the maximum value by substituting x = 1 into the function

Substitute \( x = 1 \) into \( f(x)=-4x^{2}+8x - 1 \):
\( f(1)=-4\times(1)^{2}+8\times(1)-1=-4 + 8-1=3 \).

Answer:

c. 3