topic 7. mathxl for school topic review copy 1\npart 1 of 2\na banner is hung for a party. the distance from…

topic 7. mathxl for school topic review copy 1\npart 1 of 2\na banner is hung for a party. the distance from a point on the bottom edge of the banner to the floor can be determined by using the function f(x)=0.25x² - x + 9.5, where x is the distance of the point from the left - end of the banner. how high above the floor is the lowest point on the bottom edge of the banner? explain.\nthe lowest point on the bottom edge of the banner is feet above the floor.\n(type an integer or a decimal.)

topic 7. mathxl for school topic review copy 1\npart 1 of 2\na banner is hung for a party. the distance from a point on the bottom edge of the banner to the floor can be determined by using the function f(x)=0.25x² - x + 9.5, where x is the distance of the point from the left - end of the banner. how high above the floor is the lowest point on the bottom edge of the banner? explain.\nthe lowest point on the bottom edge of the banner is feet above the floor.\n(type an integer or a decimal.)

Answer

Explanation:

Step1: Identify the function type

The function $f(x)=0.25x^{2}-x + 9.5$ is a quadratic function in the form $y = ax^{2}+bx + c$, where $a = 0.25$, $b=-1$, and $c = 9.5$.

Step2: Find the x - coordinate of the vertex

The x - coordinate of the vertex of a quadratic function $y=ax^{2}+bx + c$ is given by $x=-\frac{b}{2a}$. Substituting $a = 0.25$ and $b=-1$ into the formula, we have $x=-\frac{-1}{2\times0.25}=\frac{1}{0.5}=2$.

Step3: Find the y - coordinate of the vertex

Substitute $x = 2$ into the function $f(x)=0.25x^{2}-x + 9.5$. Then $f(2)=0.25\times2^{2}-2 + 9.5$. First, calculate $0.25\times2^{2}=0.25\times4 = 1$. Then $f(2)=1-2 + 9.5=8.5$.

Answer:

$8.5$