find the vertex.\n$f(x) = -2x^2 + 12x - 5$\n$(?, \\square)$

Answer

Explanation:

Step1: Find the x - coordinate of the vertex

For a quadratic function in the form (f(x)=ax^{2}+bx + c), the x - coordinate of the vertex is given by the formula (x =-\frac{b}{2a}). In the function (f(x)=- 2x^{2}+12x - 5), we have (a=-2) and (b = 12). Substitute (a=-2) and (b = 12) into the formula: (x=-\frac{12}{2\times(-2)}=-\frac{12}{-4}=3)

Step2: Find the y - coordinate of the vertex

Now that we know the x - coordinate of the vertex is (x = 3), we substitute (x = 3) into the function (f(x)=-2x^{2}+12x - 5) to find the y - coordinate. (f(3)=-2\times(3)^{2}+12\times3-5) First, calculate ((3)^{2}=9), then (-2\times9=-18), (12\times3 = 36). So (f(3)=-18 + 36-5=13)

Answer:

((3,13))