Question

finding maximum/minimum values with
question
find the maximum value of the function
$f(x)=-1.3x^{2}+18.4x - 58$ to the nearest hundredth.
answer
attempt 1 out of 2

Explanation:

Step1: Identify the coefficients

The quadratic function is $f(x)=- 1.3x^{2}+18.4x - 58$, where $a=-1.3$, $b = 18.4$, $c=-58$. Since $a=-1.3<0$, the parabola opens downwards and has a maximum value. The x - coordinate of the vertex of a quadratic function $y = ax^{2}+bx + c$ is given by $x=-\frac{b}{2a}$.

Step2: Calculate the x - coordinate of the vertex

$x=-\frac{18.4}{2\times(-1.3)}=\frac{18.4}{2.6}\approx7.08$

Step3: Calculate the maximum value

Substitute $x = 7.08$ into the function $f(x)=-1.3x^{2}+18.4x - 58$.
$f(7.08)=-1.3\times(7.08)^{2}+18.4\times7.08-58$
$=-1.3\times50.1264 + 130.272-58$
$=-65.16432+130.272 - 58$
$=7.10768\approx7.11$

Answer:

$7.11$